CH 11

Course 1Course 2

Chapter 11Resource Masters

Copyright © by The McGraw-Hill Companies, Inc. All rights reserved.Printed in the United States of America. Permission is granted to reproduce thematerial contained herein on the condition that such material be reproduced only forclassroom use; be provided to students, teacher, and families without charge; andbe used solely in conjunction with Glencoe Mathematics: Applications andConcepts, Course 2. Any other reproduction, for use or sale, is prohibited withoutprior written permission of the publisher.

Send all inquiries to:Glencoe/McGraw-Hill8787 Orion PlaceColumbus, OH 43240

Mathematics: Applications and Concepts, Course 2ISBN: 0-07-860118-5 Chapter 11 Resource Masters

2 3 4 5 6 7 8 9 10 047 12 11 10 09 08 07 06 05 04

Consumable Workbooks Many of the worksheets contained in the ChapterResource Masters booklets are available as consumable workbooks in bothEnglish and Spanish.

Study Guide and Intervention Workbook 0-07-860128-2

Study Guide and Intervention Workbook (Spanish) 0-07-860134-7

Practice: Skills Workbook 0-07-860129-0

Practice: Skills Workbook (Spanish) 0-07-860135-5

Practice: Word Problems Workbook 0-07-860130-4

Practice: Word Problems Workbook (Spanish) 0-07-860136-3

Answers for Workbooks The answers for Chapter 11 of theseworkbooks can be found in the back of this Chapter Resource Mastersbooklet.

StudentWorks™ This CD-ROM includes the entire Student Edition textalong with the English workbooks listed above.

TeacherWorks™ All of the materials found in this booklet are includedfor viewing and printing in the Glencoe Mathematics: Applications andConcepts, Course 2 TeacherWorks™ CD-ROM.

Spanish Assessment Masters Spanish versions of forms 2A and 2C ofthe Chapter 11 Test are available in the Glencoe Mathematics: Applicationsand Concepts Spanish Assessment Masters, Course 2 (0-07-860138-X).

iii

Vocabulary Builder .............................vii

Family Letter............................................ix

Family Activity ........................................x

Lesson 11-1Study Guide and Intervention ........................609Practice: Skills ................................................610Practice: Word Problems................................611Reading to Learn Mathematics......................612Enrichment .....................................................613








Chapter 11 AssessmentChapter 11 Test, Form 1 ........................649–650Chapter 11 Test, Form 2A......................651–652Chapter 11 Test, Form 2B......................653–654Chapter 11 Test, Form 2C......................655–656Chapter 11 Test, Form 2D......................657–658Chapter 11 Test, Form 3 ........................659–660Chapter 11 Extended Response

Assessment ...............................................661Chapter 11 Vocabulary Test/Review...............662Chapter 11 Quizzes 1 & 2..............................663Chapter 11 Quizzes 3 & 4..............................664Chapter 11 Mid-Chapter Test .........................665Chapter 11 Cumulative Review......................666Chapter 11 Standardized Test Practice..667–668

Standardized Test Practice Student Recording Sheet ..............................A1

Standardized Test Practice Rubric...................A2ANSWERS .............................................A3–A32

CONTENTS

iv

Teacher’s Guide to Using the Chapter 11 Resource Masters

The Fast File Chapter Resource system allows you to conveniently file the resources youuse most often. The Chapter 11 Resource Masters includes the core materials needed forChapter 11. These materials include worksheets, extensions, and assessment options. Theanswers for these pages appear at the back of this booklet.

All of the materials found in this booklet are included for viewing and printing in theGlencoe Mathematics: Applications and Concepts, Course 2, TeacherWorks CD-ROM.

Vocabulary Builder Pages vii-viiiinclude a student study tool that presentsup to twenty of the key vocabulary termsfrom the chapter. Students are to recorddefinitions and/or examples for each term.You may suggest that students highlight orstar the terms with which they are notfamiliar.

When to Use Give these pages to studentsbefore beginning Lesson 11-1. Encouragethem to add these pages to theirmathematics study notebook. Remind themto add definitions and examples as theycomplete each lesson.

Family Letter and Family ActivityPage ix is a letter to inform your students’families of the requirements of the chapter.The family activity on page x helps themunderstand how the mathematics studentsare learning is applicable to real life.

When to Use Give these pages to studentsto take home before beginning the chapter.

Study Guide and InterventionThere is one Study Guide and Interventionmaster for each lesson in Chapter 11.

When to Use Use these masters asreteaching activities for students who needadditional reinforcement. These pages canalso be used in conjunction with the StudentEdition as an instructional tool for studentswho have been absent.

Practice: Skills There is one master foreach lesson. These provide practice thatmore closely follows the structure of thePractice and Applications section of theStudent Edition exercises.

When to Use These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.

Practice: Word Problems There is onemaster for each lesson. These providepractice in solving word problems that applythe concepts of the lesson.

When to Use These provide additionalpractice options or may be used ashomework for second day teaching of thelesson.

Reading to Learn Mathematics Onemaster is included for each lesson. The firstsection of each master asks questions aboutthe opening paragraph of the lesson in theStudent Edition. Additional questions askstudents to interpret the context of andrelationships among terms in the lesson.Finally, students are asked to summarizewhat they have learned using variousrepresentation techniques.

When to Use This master can be used as astudy tool when presenting the lesson or asan informal reading assessment afterpresenting the lesson. It is also a helpful toolfor ELL (English Language Learner)students.

v

Enrichment There is one extensionmaster for each lesson. These activities mayextend the concepts in the lesson, offer anhistorical or multicultural look at theconcepts, or widen students’ perspectives onthe mathematics they are learning. Theseare not written exclusively for honorsstudents, but are accessible for use with alllevels of students.

When to Use These may be used as extracredit, short-term projects, or as activitiesfor days when class periods are shortened.

Assessment OptionsThe assessment masters in the Chapter 11Resources Masters offer a wide range ofassessment tools for intermediate and finalassessment. The following lists describe eachassessment master and its intended use.

Chapter AssessmentChapter Tests

• Form 1 contains multiple-choice questionsand is intended for use with basic levelstudents.

• Forms 2A and 2B contain multiple-choicequestions aimed at the average levelstudent. These tests are similar in formatto offer comparable testing situations.

• Forms 2C and 2D are composed of free-response questions aimed at the averagelevel student. These tests are similar informat to offer comparable testingsituations. Grids with axes are providedfor questions assessing graphing skills.

• Form 3 is an advanced level test withfree-response questions. Grids withoutaxes are provided for questions assessinggraphing skills.

All of the above tests include a free-responseBonus question.

• The Extended-Response Assessmentincludes performance assessment tasksthat are suitable for all students. Ascoring rubric is included for evaluationguidelines. Sample answers are providedfor assessment.

• A Vocabulary Test, suitable for allstudents, includes a list of the vocabularywords in the chapter and ten questionsassessing students’ knowledge of thoseterms. This can also be used inconjunction with one of the chapter testsor as a review worksheet.

Intermediate Assessment• Four free-response quizzes are included

to offer assessment at appropriateintervals in the chapter.

• A Mid-Chapter Test provides an optionto assess the first half of the chapter. It iscomposed of both multiple-choice and free-response questions.

Continuing Assessment• The Cumulative Review provides

students an opportunity to reinforce andretain skills as they proceed through theirstudy of Glencoe Mathematics:Applications and Concepts, Course 2. Itcan also be used as a test. This masterincludes free-response questions.

• The Standardized Test Practice offerscontinuing review of pre-algebra conceptsin various formats, which may appear onthe standardized tests that they mayencounter. This practice includes multiple-choice, short response, grid-in, andextended response questions. Bubble-inand grid-in answer sections are providedon the master.

Answers• Page A1 is an answer sheet for the

Standardized Test Practice questions thatappear in the Student Edition on pages 508–509. This improves students’familiarity with the answer formats theymay encounter in test taking.

• Detailed rubrics for assessing theextended response questions on page 509are provided on page A2.

• The answers for the lesson-by-lessonmasters are provided as reduced pageswith answers appearing in red.

• Full-size answer keys are provided for theassessment masters in this booklet.

© Glencoe/McGraw-Hill vii Mathematics: Applications and Concepts, Course 2

This is an alphabetical list of new vocabulary terms you will learn inChapter 11. As you study the chapter, complete each term’s definitionor description. Remember to add the page number where you foundthe term. Add these pages to your math study notebook to reviewvocabulary at the end of the chapter.

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn MathematicsVocabulary Builder

Vocabulary TermFound

Definition/Description/Exampleon Page

base

complex figure

height

hypotenuse[heye-PAH-tuhn-OOS]

irrational number

Vo

cab

ula

ry B

uild

er

Vocabulary TermFound

Definition/Description/Exampleon Page

leg

perfect square

Pythagorean[puh-THAG-uh-REE-uhn] Theorem

radical sign

square

square roots

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn MathematicsVocabulary Builder (continued)

© Glencoe/McGraw-Hill viii Mathematics: Applications and Concepts, Course 2

© Glencoe/McGraw-Hill ix Mathematics: Applications and Concepts, Course 2

Family LetterNAME ________________________________________ DATE ______________ PERIOD _____

Dear Parent or Guardian:

We use math skills in many of the things that we do. One of

the goals of this class is to show students how things they are

learning in the classroom are relevant to the real world. For

example, understanding area is useful in such diverse fields as

geography, navigation, sports, and architecture.

In Chapter 11, Geometry: Measuring Two-Dimensional

Figures, your child will learn how to find squares and square

roots, use the Pythagorean Theorem, and find areas of figures.

In the study of this chapter, your child will complete a variety of

daily classroom assignments and activities and possibly produce

a chapter project.

By signing this letter and returning it with your child, you agree

to encourage your child by getting involved. Enclosed is an

activity you can do with your child that also relates the math in

Chapter 11 to the real world. You may also wish to log on to

the Online Study Tools for self-check quizzes, Parent and

Student Study Guide pages, and other study help at

www.msmath2.net. If you have any questions or comments, feel

free to contact me at school.

Sincerely,

Fam

ily L

ette

r

Signature of Parent or Guardian ______________________________________ Date ________

© Glencoe/McGraw-Hill x Mathematics: Applications and Concepts, Course 2

Family ActivityNAME ________________________________________ DATE ______________ PERIOD _____

Estimating AreasWith a family member, find four small objects around the house. Puteach one on the centimeter grid and draw an outline of one side ofthe object. Estimate the area of the outline.

1. name of object: 2. name of object:

3. name of object: 4. name of object:

5. Choose one of your objects. Give a reason why you might want to find thearea of the object. Work with your family member to get ideas.

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© Glencoe/McGraw-Hill 609 Mathematics: Applications and Concepts, Course 2

a. Find the square of 5. Find the square of 16.

5 � 5 � 25 16 256

a. Find �49�. Find �169�.

7 � 7 � 49, so �49� � 7. 169 13

So, �169� � 13.

A square tile has an area of 144 square inches. What are thedimensions of the tile?

144 12 Find the square root of 144.

So, the tile measures 12 inches by 12 inches.

Find the square of each number.

1. 2 2. 9 3. 14

4. 15 5. 21 6. 45

Find each square root.

7. �16� 8. �36� 9. �256�

10. �1,024� 11. �361� 12. �484�

ENTER2nd

ENTER2nd

ENTER

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionSquares and Square Roots

The product of a number and itself is the square of the number. Numbers like 4, 25, and 2.25 arecalled perfect squares because they are squares of rational numbers. The factors multiplied to formperfect squares are called square roots. Both 5 � 5 and (�5)(�5) equal 25. So, 25 has two squareroots, 5 and �5. A radical sign, ��, is the symbol used to indicate the positive square root of anumber. So, �25� � 5.


1. 3 2. 22

3. 25 4. 24

5. 35 6. 26

7. 37 8. 50


9. �25� 10. �100�

11. �441� 12. �900�

13. �961� 14. �784�

15. �3,600� 16. �1,936�

17. What is the square of �37? 18. Find both square roots of 4,900.

19. Square 7.2. 20. Square 4.5.

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: SkillsSquares and Square Roots



NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word ProblemsSquares and Square Roots

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1. FERTILIZER John bought a bag of lawnfertilizer that will cover 400 squarefeet. What are the dimensions of thelargest square plot of lawn that the bagof fertilizer will cover?

2. GEOMETRY The area A of a circle insquare feet with a radius r in feet isgiven approximately by the formulaA � 3.14r2. What is the approximatearea of a circle with a radius of 3 feet?

3. MOTION The time t in seconds for anobject dropped from a height of h feetto hit the ground is given by the

formula t � ��23h2��. How long will it take

an object dropped from a height of 500 feet to hit the ground? Round tothe nearest tenth.

4. PACKAGING A cardboard envelope for acompact disc is a square with an areaof 171.61 square centimeters. What arethe dimensions of the envelope?

5. GEOGRAPHY Refer to the squaresbelow. They represent the approximateareas of California, Alabama, andNebraska. Find the area of Alabama.

277 mi

225 mi

395 mi

AL

NE

CA

6. Use the figure in Exercise 5. How muchlarger is California than Nebraska?


NAME ________________________________________ DATE ______________ PERIOD _____

Pre-Activity Complete the Mini Lab at the top of page 470 in your textbook.Write your answers below.

1. On grid paper, draw and label three other rectangles that have a perimeter of 16 units.

2. Summarize the dimensions and areas of the rectangles that you drew in a table like the one shown below.

3. Draw three different rectangles that have a perimeter of12 units and find their areas.

4. What do you notice about the rectangles with the greatest areas?

Reading the Lesson 5. In this lesson, the word square is used in several different ways. Tell the

meaning of the word as it is used in each phrase or sentence.a. Find the square of 3.

b. 9 units squared

c. A boxing ring is a square with an area of 400 ft2.

Helping You Remember6. Work with a partner. Use a calculator to find the squares of six numbers,

some of them decimals. Then write only the squares in a list andexchange lists with your partner. Find the square roots of the squares inthe list that you receive. Write your answers in the form �x� � y.

5 units1 unit

4 units2 units

3 units

3 units

5 square units8 square units

9 square units

2 � 6 12

16

3 � 5

4 � 4

15

1 � 7 7

Drawing Dimensions (units) Area (sq units)

6 units

2 units

5 units

3 units

4 units

4 units

Reading to Learn MathematicsSquares and Square Roots


The Geometric MeanThe square root of the product of two numbers is called their geometric mean.The geometric mean of 12 and 48 is �12 � 4�8� � �576� or 24.

Find the geometric mean for each pair of numbers.

1. 2 and 8 2. 4 and 9 3. 9 and 16

4. 16 and 4 5. 16 and 36 6. 12 and 3

7. 18 and 8 8. 2 and 18 9. 27 and 12

Recall the definition of a geometric sequence. Each term is found bymultiplying the previous term by the same number. A missing term in ageometric sequence equals the geometric mean of the two terms on eitherside.

Find the missing term in each geometric sequence.

10. 4, 12, , 108, 324 11. 10, , 62.5, 156.25, 390.625

12. 1, 0.4, , 0.064, 0.0256 13. 700, 70, 7, 0.7, , 0.007

14. 6, , 24 15. 18, , 32??

??

??

EnrichmentNAME ________________________________________ DATE ______________ PERIOD _____

Enrichment

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Estimate �40� to the nearest whole number.

List some perfect squares.

1, 4, 9, 16, 25, 36, 49, …

36 � 40 � 49 40 is between the perfect squares 36 and 49.

�36� � �40� � �49� Find the square root of each number.

6 � �40� � 7 �36� � 6 and �49� � 7

So, �40� is between 6 and 7. Since 40 is closer to 36 than to 49, the best whole numberestimate is 6.

Use a calculator to find the value of �28� tothe nearest tenth.

28 5.291502622

�28� � 5.3

Check Since 52 � 25 and 25 is close to 28, the answer is reasonable.

Estimate each square root to the nearest whole number.

1. �3� 2. �8�

3. �26� 4. �41�

5. �61� 6. �94�

7. �152� 8. �850�

Use a calculator to find each square root to the nearest tenth.

9. �2� 10. �27�

11. �73� 12. �82�

13. �105� 14. �395�

15. �846� 16. �2,298�

ENTER2nd

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionEstimating Square Roots

Recall that a perfect square is a square of a rational number. In Lesson 5-8, you learned that anynumber that can be written as a fraction is a rational number. A number that cannot be written as afraction is an irrational number.

0 1 2 3 4 5 6

28

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1. �5� 2. �10� 3. �21�

4. �28� 5. �78� 6. �102�

7. �179� 8. �274� 9. �303�

10. �563� 11. �592� 12. �755�

13. �981� 14. �1,356� 15. �1,688�

16. �3,287� 17. �3,985� 18. �4,125�


19. �6� 20. �19� 21. �30�

22. �77� 23. �114� 24. �125�

25. �149� 26. �182� 27. �212�

28. �436� 29. �621� 30. �853�

31. �918� 32. �1,004� 33. �1,270�

34. �5,438� 35. �4,215� 36. �5,786�

37. Order �275�, 4.91, and �23� from least to greatest.

38. Graph �42� and �62� on the same number line.

0 1 2 3 4 5 876

Practice: SkillsEstimating Square Roots

NAME ________________________________________ DATE ______________ PERIOD _____

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word ProblemsEstimating Square Roots


1. GEOMETRY The diameter d of a circlewith area A is given by the formula

d � ��4�A��. What is the diameter of a

circle with an area of 56 square inches?Use 3.14 for � and round to the nearesttenth.

2. FENCING Carmen wants to buy fencingto enclose a square garden with anarea of 500 square feet. How muchfencing does Carmen need to buy?Round to the nearest tenth.

3. OCEANS The speed v in feet per secondof an ocean wave in shallow water ofdepth d in feet is given by the formulav � �32d�. What is the speed of anocean wave at a depth of 10 feet?Round to the nearest tenth.

4. LIGHTING A new flashlight has a beamwhose width w at a distance d from theflashlight is given by the formulaw � 1.2�d�. What is the width of thebeam at a distance of 30 feet? Round tothe nearest tenth.

5. SOUND The speed of sound in air c inmeters per second at a temperature Tin degrees Celsius is givenapproximately by the formula c � �402(T�� 273�)�. What is the speedof sound in air at a temperature of 25 degrees Celsius? Round to thenearest tenth.

6. PROJECTILES The muzzle velocity v infeet per second necessary for a cannonto hit a target x feet away is estimatedby the formula v � �32x�. What muzzlevelocity is required to hit a target3,000 feet away? Round to the nearesttenth.

3,000 ft


Pre-Activity Complete the Mini Lab at the top of page 475 in your textbook.Write your answers below.Use algebra tiles to estimate the square root of each number tothe nearest whole number.

1. 40 2. 28 3. 85 4. 62

5. Describe another method that you could use to estimate the square rootof a number.

Reading the Lesson

6. Why is �4� a rational number and �2� an irrational number?

7. How do you read the statement �64� � �75� � �81�?

8. Why are �64� and �81� used in Example 1?

Helping You Remember9. The key to estimating square roots without a calculator is to be familiar

with common perfect squares. Complete the following table of commonperfect squares then test yourself to see how many you can rememberwithout using a calculator.

Reading to Learn MathematicsEstimating Square Roots

NAME ________________________________________ DATE ______________ PERIOD _____

Number 5 6 7 8 9 10 11 12 13 14 15 16 20 25

Square 25

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World Series RecordsEach problem gives the name of a famous baseball player. To findwho set each record, graph the points on the number line.

1. pitched 23 strikeouts in one World Series

U at �3�, X at 3.3, K at 0.75, O at �32�, F at �6�, A at 2�

78�

2. 71 base hits in his appearances in World Series

B at �5�, R at �12�, A at 3.75, G at �1163�

, E at �52�, Y at 0.375, R at �

143�,

I at 1.6, and O at 0.7�

3. 10 runs in a single World Series

N at �60�, K at �30�, A at 4.3, S at 6.2, C at �496�, O at �45�, and J at �17�

4. batting average of 0.625 in a single World Series

E at �32�, U at 6�56�, A at �

134�, T at �55�, B at 5.3, R at �40�, H at 7.75,

B at �251�

5. 42 World Series runs in his career

E at �140�, Y at 9.6, I at 8.6, E at �90�, A at �221�, M at �70�, C at 8�

78�,

M at �100�, N at 10.7, K at 9�111�

, T at �120�, L at 11.4

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


0 4321

4 8765

0 4321

4 8765

8 1211109

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Find the missing measure of a right triangle if a � 4 inches and b � 3 inches.

c2 � a2 � b2 Pythagorean Theorem

c2 � 42 � 32 Replace a with 4 and b with 3.

c2 � 16 � 9 Evaluate 42 and 32.

c2 � 25 Add.

�c2� � �25� Take the square root of each side.

c � 5 Simplify.

The length of the hypotenuse is 5 inches.

Determine whether a triangle with side lengths of 6 meters,9 meters, and 12 meters is a right triangle.

c2 � a2 � b2 Pythagorean Theorem

122 � 62 � 92 Replace a with 6, b with 9, and c with 12.

144 � 36 � 81 Simplify.

144 117 Add.

The triangle is not a right triangle.

Find the missing measure of each right triangle. Round to the nearesttenth if necessary.

1. 2. 3.

Determine whether each triangle with the given side lengths is aright triangle. Write yes or no.

4. 15 ft, 8 ft, 17 ft 5. 5 in., 13 in., 17 in. 6. 9 yd, 40 yd, 41 yd

13 cm

16 cm

a cm5 m

7.5 m

c m

9 in.

4 in.c in.

3 in.

4 in.c in.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionThe Pythagorean Theorem

The sides of a right triangle have special names. The sides adjacent to the right angle are the legs. The side opposite the right angle is the c2 � a2 � b2

hypotenuse. The Pythagorean Theorem describes the relationship between the length of the hypotenuse and the lengths of the legs. In a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the legs.

b

ac

Find the missing measure of each right triangle. Round to the nearesttenth if necessary.

1. 2.

3. 4.

5. 6.

7. 8.

9. a � 15 cm, b � 20 cm 10. a � 2 yd, b � 12 yd

11. a � 13 in., c � 16.5 in. 12. b � 8 mm, c � 17 mm

13. a � 1.3 ft, b � 4.6 ft 14. a � 14.7 m, c � 23 m

Determine whether each triangle with the given side lengths is aright triangle. Write yes or no.

15. 10 ft, 24 ft, 26 ft 16. 5 in., 8 in., 9 in.

17. 6 cm, 9 cm, 12 cm 18. 4.5 mm, 6.0 mm, 7.5 mm

14 mmc mm

6.7 mm

11.2 m

6 m

a m

2.7 yd 3 yd

a yd

20.3 in. 32 in.

c in.

20 cm

26 cmx cm12.4 ft

a ft

15 ft

5 in.

c in.

5 in.7 m

b m

20 m

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: SkillsThe Pythagorean Theorem



Practice: Word ProblemsThe Pythagorean Theorem

NAME ________________________________________ DATE ______________ PERIOD _____

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1. ORIGAMI Chee has a piece of papermeasuring 8.5 inches by 8.5 inches. Ifshe folds the paper diagonally in half,how long is the folded side? Round tothe nearest tenth.

2. COMPUTERS In a computer catalog,a computer monitor is said to be 19 inches. This distance is the diagonaldistance across the screen. If the screenis 10 inches high, what is the width ofthe screen? Round to the nearest tenth.

3. ANTENNAS A wire 10 meters long issupporting a utility pole. The wire isanchored to the ground and is attachedto the pole 9 meters above the ground.What is the distance from the bottom ofthe pole to the point where the wire isattached to the ground? Round to thenearest tenth.

9 m10 m

x m

4. RAMPS Crystal wants to build a rampthat will rise 4 feet over a horizontaldistance of 20 feet. How long will theramp be? Round to the nearest tenth.

4 ft

20 ft

x ft

5. POOLS Salomon swims diagonallyacross his pool every day. If Salomon’spool is 4 meters wide and 16 metersdiagonally across, how long is his pool,to the nearest tenth of a meter?

6. FRAMES Rosa has a picture frame thatmeasures 12 inches by 18 inches. Whatis the diagonal distance across theframe? Round to the nearest tenth.

Pre-Activity Read the introduction at the top of page 479 in your textbook.Write your answers below.

1. Can the mirror fit through the doorway? Explain.

2. Make a scale drawing on grid paper to solve the problem.

Reading the Lesson3. In the Pythagorean Theorem c2 � a2 � b2, which letter represents

the length of the hypotenuse?

4. How do you know that the diagonal of a rectangle is the hypotenuse oftwo right triangles?

5. In Examples 4 and 5 on page 481, how do you know which length is c?

Helping You Remember6. Summarize what you learned in this lesson by labeling the sides of the

right triangle with the letters a, b, and c and then completing the table.

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn MathematicsThe Pythagorean Theorem


You canfind

If you knowthe lengths

a

b

c


Pythagoras in the AirIn the diagram at the right, an airplane heads north at 180 mi/h.But, the wind is blowing towards the east at 30 mi/h. So, theairplane is really traveling east of north. The middle arrow in thediagram shows the actual direction of the airplane.

The actual speed of the plane can be found using the PythagoreanTheorem.

�302 �� 1802� � �900 �� 32,40�0�

� �33,30�0�

� 182.5

The plane’s actual speed is about 182.5 mi/h.

Find the actual speed of each airplane. Round answers to the nearesttenth. (You might wish to draw a diagram to help you solve theproblem.)

1. An airplane travels at 240 mi/h east. 2. An airplane travels at 620 mi/h west.A wind is blowing at 20 mi/h toward A wind is blowing at 35 mi/h towardthe south. the south.

3. An airplane travels at 450 mi/h south. 4. An airplane travels at 1,200 mi/h east.A wind is blowing at 40 mi/h toward A wind is blowing at 30 mi/h towardthe east. the north.


E

N(not drawn to scale)

180 mi/h

30 mi/h

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Find the area of a parallelogram if the base is 6 inches and the height is 3.7 inches.

Estimate A � 6 � 4 or 24 in2

A � bh Area of a parallelogram

A � 6 � 3.7 Replace b with 6 and h with 3.7.

A � 22.2 Multiply.

The area of the parallelogram is 22.2 square inches. This is close to the estimate.

Find the area of the parallelogram at the right.

Estimate A � 10 � 10 or 100 cm2

A � bh Area of a parallelogram

A � 12 � 8 Replace b with 12 and h with 8.

A � 96 Multiply.

The area of the parallelogram is 96 square centimeters. This is close to the estimate.

Find the area of each parallelogram. Round to the nearest tenth ifnecessary.

1. 2. 3. 17 in.

16 in.

4.6 mm

8 mm

5 ft

13.2 ft

12 cm

8 cm

3.7 in.

6 in.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionArea of Parallelograms

The area A of a parallelogram equals the product of its base b and its height h.

A � bh

The base is any side of a parallelogram.

The height is the length ofthe segment perpendicularto the base with endpointson opposite sides.

b

h

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Find the area of each parallelogram. Round to the nearest tenth ifnecessary.

1. base � 5 ft 2. base � 9 in.height � 12 ft height � 2 in.

3. base � 6 cm 4. base � 4�25� yd

height � 5.5 cm height � 2 yd

5. base � 15.3 mm 6. base � 19.6 mheight � 8 mm height � 14.5 m

7. 8.

9. 10.

11. 12.

13. 14.

7 yd

24 ft

4.3 mm

12 mm

20 in.

11 in.45

2.3 cm

2 cm

12 ft

9 ft15 mm

11 mm

7 in.

4 in.

2 cm

3 cm

Practice: SkillsArea of Parallelograms

NAME ________________________________________ DATE ______________ PERIOD _____

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word ProblemsArea of Parallelograms


1. SAILS Joyce wants to construct a sailwith the dimensions shown. How muchmaterial will be used?

14 ft

25 ft

2. SIGNS Pedro wants to make the sign inthe shape shown and needs to knowhow much material will be needed.What is the area of the sign?

30 in.

35 in.

YardSale

3. SHADING Alma’s engineering firm mustdetermine the area of the largestnoontime shadow that a proposedbuilding design will create. What is thearea of the shadow?

40 ft

56 ft

4. POOLS Tamika has designed a pool inthe shape shown. What is the area ofthe bottom of the pool if the surface isperfectly flat?

30 m20 m

5. CITY PLANNING Two parallel streets arecut across by two other parallel streetsas shown in the figure, cutting off aparcel of land in the shape of aparallelogram. Find the area of theparcel of land.

250 ft

340 ft

Main Street

Dresden Way

Colu

mbu

s Av

e.

Jeffe

rson

Ave

.

6. TARPS Neka wants to cut a tarp in theshape shown. What is the minimumamount of canvas cloth that he willneed?

36 ft

40 ft



1. What is the value of x and y for each parallelogram?

2. Count the grid squares to find the area of each parallelogram.

3. On grid paper, draw three different parallelograms in which x � 5 unitsand y � 4 units. Find the area of each.

4. Make a conjecture about how to find the area of a parallelogram if youknow the values of x and y.

Reading the Lesson5. Explain how to find the height of a parallelogram.

6. Suppose you are asked to find the area of the parallelogram below. Is thegiven solution correct? Explain.

A � bhA � 12 � 5A � 60The area of the parallelogram is 60 square centimeters.

Helping You Remember7. Because rectangles, rhombuses, and squares are all parallelograms, the

formula for finding the area of a parallelogram is also used to find theareas of each of these figures. Think of a way to remember that the areaof a parallelogram is the product of its base and height. For example,draw several parallelograms, rectangles, rhombuses, and squares andlabel the base and height for each. Write the formula for the area beloweach model.

3 cm5 cm

12 cm

Reading to Learn MathematicsArea of Parallelograms

NAME ________________________________________ DATE ______________ PERIOD _____

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Two Area PuzzlesCut out the five puzzle pieces at the bottom of this page. Then usethem to solve these two puzzles.

1. Use all five puzzle pieces to make 2. Use the four largest pieces to makea square with an area of 9 square a square with an area of 8 squareinches. Record your solution below. inches. Record your solution below.

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


2 in.

1 in.

1 in.

2 in.

2 in.

1 in2

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Find the area of the triangle.Estimate �

12

�(6)(5) � 15

A � �12�bh Area of a triangle

A � �12�6 � 4.5 Replace b with 6 and h with 4.5.

A � 13.5 Multiply.

The area of the triangle is 13.5 square inches. This is close to the estimate.

Find the area of the trapezoid.

A � �12�h(b1 � b2) Area of a trapezoid

A � �12�(4)(3 � 6) Replace h with 4, b1 with 3, and b2 with 6.

A � 18 Simplify.

The area of the trapezoid is 18 square centimeters.

Find the area of each figure. Round to the nearest tenth if necessary.

1. 2. 3. 4. 8 cm

13.5 cm

18 cm

7 in.

5 in.

14 in.

7 mm

9 mm12 ft

7 ft

4 cm

3 cm

6 cm

4.5 in.

6 in.

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionArea of Triangles and Trapezoids

The area A of a triangle equals half the product of its base b and its height h.

A � �12�bh

A trapezoid has two bases, b1 and b2. The height of a trapezoid is the distance between the two bases. The area A of a trapezoid equals half the product of the height h and the sum of the bases b1 and b2.

A � �12�h(b1 � b2)

b1

b2

h

The base of atriangle can beany of its sides.

The height is thedistance from a baseto the opposite vertex.

b

h


1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. triangle: base � 16 cm, height � 9.4 cm

12. triangle: base � 13.5 in., height � 6.4 in.

13. trapezoid: bases 22.8 mm and 19.7 mm, height 36 mm

14. trapezoid: bases 5 ft and 3�12� yd, height 7 ft

14 mm

3.8 mm

15.3 mm

7.5 cm

12.2 cm

5.6 in.

6.9 in.12 ft

20.1 ft

25 ft

24 mm

20.7 mm7 cm

9.2 cm

2 cm

4 ft

3 ft

6.5 ft

12 mm

18 mm

10 mm

3 ft

2 ft10 cm

9 cm

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: SkillsArea of Triangles and Trapezoids



Practice: Word ProblemsArea of Triangles and Trapezoids

NAME ________________________________________ DATE ______________ PERIOD _____

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51. GEOGRAPHY Arkansas has a shape thatis similar to a trapezoid with bases ofabout 182 miles and 267 miles and aheight of about 254 miles. Estimate thearea of the state.

2. PATIOS Greta is making a patio withthe dimensions given in the figure.What is the area of the patio?

172.5 ft2

15 ft

15 ft

8 ft

3. FLAGS Malila wants to make theInternational Marine Signal flag shownwhich represents the number six. Whatis the area of the flag?

30 in.100 in. 5 in.

4. SIGNS Estimate the area of the yieldsign.

390 in2

30 in.

26 in.

5. TILING A ceramics company wants toproduce tiles in the shape shown. Whatis the area of the surface of each tile?

8.5 cm

8.5 cm

6. GARDENING Kinu wants to buy topsoilfor a section of her garden that has thedimensions shown in the figure. Whatis the area of this section of Kinu’sgarden?

7 yd2

4 yd

3.5 yd

4 yd


1. What is the area of the parallelogram?

2. Cut along the diagonal. What is true about the triangles formed?

3. What is the area of each triangle?

4. If the area of a parallelogram is bh, then write an expression for the areaA of each of the two congruent triangles that form the parallelogram.

Reading the Lesson5. In a triangle, which side is the base?

6. How do you find the height of a triangle?

7. For what kind of triangle might the height be found outside of thetriangle?

8. How is the height of a trapezoid similar to the height of a triangle orparallelogram?

Helping You Remember9. The Mini Lab in this lesson gave you a good way to remember the

formula for the area of a triangle by showing you that it is half the areaof a parallelogram, so A � �

12�bh. Think of a way to help you remember the

formula for the area of a trapezoid. Do you recognize anything in the

formula A � �12�h(b1 � b2)?

NAME ________________________________________ DATE ______________ PERIOD _____

Reading to Learn MathematicsArea of Triangles and Trapezoids



Heron’s FormulaA formula named after Heron of Alexandria, Egypt, can be used to findthe area of a triangle given the lengths of its sides.

Heron’s formula states that the area A of a triangle whose sides measurea, b, and c is given by

A � �s(s�a�)(s�b)�(s�c)�,

where s is the semiperimeter:

s � �a �

2b � c�.

Estimate the area of each triangle by finding the mean of the innerand outer measures. Then use Heron’s Formula to compute a moreexact area. Give each answer to the nearest tenth of a square unit.

1. 2. 3.

Estimated area: Estimated area: Estimated area:

Computed area: Computed area: Computed area:

4. 5. 6.

Estimated area: Estimated area: Estimated area:

Computed area: Computed area: Computed area:

9

57

8

83

7

77

6

8

109

9

106

66


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Find the area of the circle.

A � �r2 Area of circle

A � � � 52 Replace r with 5.

5 78.53981634

The area of the circle is approximately 78.5 square centimeters.

Find the area of a circle that has a diameter of 9.4 millimeters.

A � �r2 Area of a circle

A � � � 4.72 Replace r with 9.4 2 or 4.7.

A � 69.4 Use a calculator.

The area of the circle is approximately 69.4 square millimeters.

Find the area of each circle. Round to the nearest tenth.

1. 2. 3.

4. radius � 2.6 cm 5. radius � 14.3 in. 6. diameter � 5�12� yd

7. diameter � 4�34

� mi 8. diameter � 7.9 mm 9. radius � 2�15� ft

12 ft

25 mm7 in.

ENTER��

5 cm

NAME ________________________________________ DATE ______________ PERIOD _____

Study Guide and InterventionArea of Circles

The area A of a circle equals the product of pi (�) and the square of its radius r.

A � �r 2

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1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. radius � 5.7 mm 12. radius � 8.2 ft

13. diameter � 3�14� in. 14. diameter � 15.6 cm

15. radius � 1.1 in. 16. diameter � 12�34� yd

11.9 ft2.1 mm

22.5 in.

4.7 yd

8 cm4.3 ft

14 in.35 mm

4 yd

1 cm

Practice: SkillsArea of Circles

NAME ________________________________________ DATE ______________ PERIOD _____

NAME ________________________________________ DATE ______________ PERIOD _____

Practice: Word ProblemsArea of Circles


1. POOLS Susan designed a circular poolwith a diameter of 25 meters. What isthe area of the bottom of the pool?Round to the nearest tenth.

2. MONEY Find the area of the coin to thenearest tenth.

19 mm

3. DRUMS What is the area of thedrumhead on the drum shown below?Round to the nearest tenth.

14 in.

4. PIZZA Estimate the area of the top of around pizza that has a diameter of16 inches. Round to the nearest tenth.

5. GARDENING Jane needs to buy mulchfor the garden with the dimensionsshown in the figure. For how much areadoes Jane need to buy mulch? Round tothe nearest tenth.

5.5 yd

6. UTILITIES What is the area of the topsurface of a circular manhole cover thathas a radius of 30 centimeters? Roundto the nearest tenth.



1. What is the measurement of the base and the height?

2. Substitute these values into the formula for the area of a parallelogram.

3. Replace C with the expression for the circumference of a circle, 2�r.Simplify the equation and describe what it represents.

Reading the Lesson4. The formula for the area of a circle uses the number �. How does this

affect the value of the area of a circle found using the formula?

5. If you are given the length of the diameter of a circle, how can you find itsarea?

Helping You Remember6. Think about the formulas you have learned that involve circles: C � 2�r

or C � �d and A � �r2. To help you remember the difference between theformulas for circumference and the formula for area, think about thedifferences in the units used for each measurement. What kinds of unitsare used for each? How can this help you remember the formula for thearea of a circle?

Reading to Learn MathematicsArea of Circles

NAME ________________________________________ DATE ______________ PERIOD _____

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Seki KowaJapanese mathematician Seki Kowa (c. 1642–1708) is called The Arithmetical Sage because of his many contributions to the development of mathematics in Japan. Before Seki, mathematics in Japan was considered a form of art to be enjoyed by intellectuals in their leisure time. Seki demonstrated the practical uses of mathematics and introduced social reforms that made it possible for anyone, not just intellectuals, to study mathematics.

One of Seki’s contributions to mathematics was his calculation of a valueof � that was correct to eighteen decimal places.

� � 3.141592653589793238…

Seki had noticed the phenomenon that you see at the right: as thenumber of sides of a regular polygon increases, the polygon looksmore and more like a circle. So, Seki calculated the following ratiofor polygons of increasingly many sides.

As the number of sides of the polygon gets larger, this ratio must getcloser to the ratio of the circumference of the circle to the diameter ofthe circle. This ratio, of course, is �.

You are given information below about a regular polygon and thecircle drawn around the polygon. Use a calculator to find Seki’sratio. (Give as many decimal places as there are in your calculator display.) What do you notice about your answers?

1. length of one side � 5 2. length of one side � 4.5922number of sides � 6 number of sides � 8diameter of circle � 10 diameter of circle � 12

3. length of one side � 3.7544 4. length of one side � 37.5443number of sides � 20 number of sides � 20diameter of circle � 24 diameter of circle � 240

5. length of one side � 1.6754 6. length of one side � 2.6389number of sides � 150 number of sides � 500diameter of circle � 80 diameter of circle � 420

perimeter of regular polygon��diameter of circle drawn around the polygon

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


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Study Guide and InterventionArea of Complex Figures

Find the area of the figure at the rightin square feet.

The figure can be separated into a rectangle and a trapezoid. Find the area of each.

Area of Rectangle

A � �w Area of a rectangle

A � 12 � 8 Replace � with 12 and w with 8.

A � 96 Multiply.

Area of Trapezoid

A � �12�h(b1 � b2) Area of a trapezoid

A � �12�(4)(4 � 12) Replace h with 4, b1 with 4, and b2 with 12.

A � 32 Multiply.

The area of the figure is 96 � 32 or 128 square feet.


1. 2.

3. 18 mm

38 mm

11 mm

4 in. 5 in.

4 cm

6.5 cm

13 cm

6 cm

6 cm

12 ft

4 ft

4 ft

12 ft

8 ft

12 ft

4 ft

4 ft

8 ft

NAME ________________________________________ DATE ______________ PERIOD _____

Complex figures are made of circles, rectangles, squares, and other two-dimensional figures. To findthe area of a complex figure, separate it into figures whose areas you know how to find, and then addthe areas.


Practice: SkillsArea of Complex Figures


1. 2.

3. 4.

5. 6.

7. 8.1.3 ft

1.3 ft

3.5 ft

3.5 ft

3.5 ft

3.5 ft4 m

4 m

2 m

2 m

2 m

20 yd

9 yd11 yd

9 yd

4 yd 4 yd

13 m

9 m

7 m

3 in. 4 in.

9 in.15 in.

5 in.

10 in.

30 in.

15 in.

7 mm5 mm

6 mm

7 cm

7 cm

NAME ________________________________________ DATE ______________ PERIOD _____


Practice: Word ProblemsArea of Complex Figures

ARCHITECTURE For Exercises 1–6 use Jaco’spreliminary design of his vacation house at the right. Round to the nearest tenth ifnecessary.

8 ft4 ft

4 ft

4 ft

8 ft 4 ft

4 ft

4 ft

8 ft

8 ft 4 ft4 ft

2 ft

4 ft12 ft 4 ft

12 ft

16 ft

16 ft12 ft

16 ft

16 ft

4 ft 4 ft

bedroom1

kitchen bedroom2

bathroom

livingroomden

NAME ________________________________________ DATE ______________ PERIOD _____

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1. What type of figure is bedroom 1? Findthe area of bedroom 1.

2. What is the area of the bedroom 2?What figures did you use to find thearea?

3. What is the area of the bathroom?What are the dimensions of the figuresyou used to find this area?

4. What is the area of the living room?How many figures did you use to findthis area?

5. What is the area of the den? Whatwould the area of the den be if thesemicircular window were removed andreplaced with a flat window?

6. What is the area of the kitchen? If Jacoadds a rectangular cooking island inthe middle of the kitchen withdimensions 6 feet by 4 feet, how manysquare feet of walking space will beleft?


Reading to Learn MathematicsArea of Complex Figures

Pre-Activity Read the introduction at the top of page 498 in your textbook.Write your answers below.

1. Describe the shape of the kitchen.

2. How could you determine the area of the kitchen?

3. How could you determine the total square footage of a house with rooms shapedlike these?

Reading the Lesson4. Look up the term footage in a dictionary. Write the meaning that matches

the way the term is used in this lesson.

5. What do you think the term square footage means?

6. Which word of the compound square footage indicates area? Explain.

7. Look up the term two-dimensional in a dictionary.

8. Name two dimensions of each of the following figures.

a. rectangle b. parallelogram c. triangle

9. Refer to the figure in Example 2 on page 499. How do you know that the baseand height of the triangle are each 4 inches long?

Helping You Remember10. Look in a dictionary for the meanings of the word complex when used as

an adjective. Write the meaning of the word as it is used in this lesson.Why can the figures in Examples 1 and 2 be considered complex figures?

NAME ________________________________________ DATE ______________ PERIOD _____


Extending the Pythagorean TheoremThe Pythagorean Theorem says that the sum of the areas of thetwo smaller squares is equal to the area of the largest square.Show that the Pythagorean Theorem can be extended to includeother shapes on the sides of a triangle. To do so, find the areas ofthe two smaller shapes. Then, check that their sum equals thearea of the largest shape.

1. area of smallest shape: 2. area of smallest shape:

area of middle shape: area of middle shape:

area of largest shape: area of largest shape:

3. area of smallest shape: 4. area of smallest shape:

area of middle shape: area of middle shape:

area of largest shape: area of largest shape:

3 in.

3 in.

3 in.

5 in.

5 in.

5 in.

4 in.

4 in.4 in.

3 in.

3 in.

5 in.5 in.

4 in.

4 in.

1.5in.

3 in.

5 in.

4 in.

2.5 in.

2 in.

5 in.

4 in.

3 in.

55

44 3

3


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Study Guide and InterventionArea Models and Probability

A randomly-dropped counter falls somewhere in the squares. Find the probability that it falls on the shaded squares.

probability �

�

Area of Shaded Squares Area of All Squares

A � �r2 Area of a circle A � �12�bh Area of a triangle

A � � � 12 r � 1 A � �12�(5)(6) b � 5 and h � 6

A � 3.1 Simplify. A � 15 Simplify.

So, the probability of a counter falling in the shaded squares is about �31.51� or

about 20.7%.

A randomly-dropped counter falls in the squares. Find theprobability that it falls in the shaded squares. Write as a percent.Round to the nearest tenth if necessary.

1. 2. 3.

4. 5. 6.

area of shaded squares��area of all squares

number of ways to land in shaded squares��number of ways to land on squares

NAME ________________________________________ DATE ______________ PERIOD _____

You can relate probability to the area of geometric shapes.

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Practice: SkillsArea Models and Probability

A randomly-dropped counter falls in the squares. Find theprobability that it falls in the shaded squares. Write as a percent.Round to the nearest tenth if necessary.

1. 2.

3. 4.

5. 6.

7. 8.

NAME ________________________________________ DATE ______________ PERIOD _____


Practice: Word ProblemsArea Models and Probability

GAMES Each figure represents a square dartboard. If it is equallylikely that a thrown dart will land anywhere on the dartboard, findthe probability that it lands in the shaded region. Round to thenearest tenth.

NAME ________________________________________ DATE ______________ PERIOD _____

1. 2.

17.5%

3. 4.

9.6%

5 cm

30 cm

10 cm

2 in.

12 in.

2 in.

4 in.

8 in.

12 in.

4 in.11.3 in.

16 in.


Reading to Learn MathematicsArea Models and Probability


1. Do certain products occur more often?

2. Make and complete the table below to find all the possible outcomes.

Reading the Lesson3. How can you use the grid following the introduction in your textbook to

determine that the probability of rolling two numbers whose product is 6or 12 is �

29�?

4. The formula for probability is �detostiraeldar

aeraea

�. How does this lesson simplify

the expression for probability?

Helping You Remember5. Find the dimensions of a target for darts or for a bow and arrow. Draw a

model that shows the measurements. Then show the probability of hittingthe area that scores the most points per hit.

NAME ________________________________________ DATE ______________ PERIOD _____

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� 1 2 3 4 5 6

1 1 2 3

2 2 4 6

3

4

5

6

Area Formulas for Regular PolygonsRecall that the sides of a regular polygon are all the same length. Here aresome area formulas for four of the regular polygons. The variable s standsfor the length of one side.

triangle pentagon hexagon octagon

A � �s42� �3� A � �

s42� �25 � 1�0�5�� A � �

32s2� �3� A � 2s2(�2� � 1)

Find the area of each polygon with the side of given length. Use acalculator and round each answer to the nearest tenth.

1.

2.

3.

4.

Now use the table above to find the area of each shaded region below.Unless otherwise specified, each segment is 1 centimeter long.

5. 6. 7.

8. 9. 10.

NAME ________________________________________ DATE ______________ PERIOD _____

Enrichment


Length ofa Side

Triangle Pentagon Hexagon Octagon

1 cm

2 cm

3 cm

4 cm

2 cm2 cm

3 cm

Write the letter for the correct answer in the blank at the right of each question.

1. Find 52.A. 10 B. 25 C. 52 D. 7 1.

2. Find 182.F. 36 G. 162 H. 18 I. 324 2.

3. Find �2,500�.A. 50 B. 500 C. 1,250 D. 250 3.

4. Estimate �37� to the nearest whole number.F. 18 G. 19 H. 7 I. 6 4.

5. Estimate �143� to the nearest whole number.A. 10 B. 11 C. 12 D. 20,499 5.


7. Use a calculator to find �43� to the nearest tenth.A. 1,849 B. 6.6 C. 6.5 D. 3.5 7.

8. The lengths of the legs of a right triangle are 8 centimeters and6 centimeters. Which equation would you solve to find the length ofthe hypotenuse?F. 62 � x2 � 82 G. 82 � x2 � 62 H. 62 � 82 � x2 I. 82 � 62 � x2 8.

9. The length of the hypotenuse of a right triangle is 20 feet, and the lengthof one leg is 16 feet. Find the length of the other leg.A. 12 ft B. 72 ft C. 26 ft D. 36 ft 9.

10. Which could be the lengths of the sides of a right triangle?F. 6 m, 8 m, 9 m G. 11 ft, 12 ft, 14 ftH. 30 cm, 40 cm, 50 cm I. 3 cm, 4 cm, 7 cm 10.

11. ART A rectangular picture frame is 24 inches long by 18 inches wide. Adiagonal brace is nailed across the back of the frame from one corner tothe other. How long is the brace?A. 30 in. B. 42 in. C. 45 in. D. 21 in. 11.

12. What is the area of a parallelogram with a height of 4 yards and a baseof 5 yards?F. 80 yd2 G. 10 yd2 H. �

45� yd2 I. 20 yd2 12.

13. Find the area of a circle with a radius of 6 feet. Round to the nearest tenth.A. 113.1 ft2 B. 18.8 ft2 C. 452.4 ft2 D. 37.7 ft2 13.

Chapter 11 Test, Form 1


Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Ass

essm

ent


14.F. 5,026.5 m2 G. 125.7 m2

H. 1,256.6 m2 I. 62.8 m2 14.

15.A. 47 m2 B. 75 m2

C. 60 m2 D. 165 m2 15.

16.F. 104.5 m2 G. 660 m2

H. 330 m2 I. 225.5 m2 16.

17.A. 15 in2 B. 50 in2

C. 2 in2 D. 500 in2 17.

18.F. 56 m2 G. 144 m2

H. 2,560 m2 I. 104 m2 18.

A randomly-dropped counter falls in the squares. Find the probability that it falls in the shaded squares. Write as a percent. Round to the nearest tenth if necessary.

19.A. 21.7% B. 16.7%C. 12.2% D. 5.0% 19.

20.F. 8.3% G. 50%H. 25% I. 20% 20.

Bonus Find ��121�. B:

8 m

8 m

10 m

10 in.

5 in.

41 m

19 m

11 m

8 m

15 m

10 m

40 m

NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 11 Test, Form 1 (continued)



1. Find 102.A. 12 B. 20 C. 1,000 D. 100 1.

2. Find 422.F. 1,008 G. 420 H. 1,764 I. 84 2.

3. Find �841�.A. 29 B. 210 C. 52 D. 31 3.


5. Estimate �178� to the nearest whole number.A. 14 B. 13 C. 12 D. 19 5.

6. Estimate �1,001� to the nearest whole number.F. 31 G. 32 H. 33 I. 20 6.

7. Use a calculator to find �267� to the nearest tenth.A. 17.4 B. 16.7 C. 71,289 D. 16.3 7.

8. The lengths of the legs of a right triangle are 22 feet and 19 feet. Whichequation would you solve to find the length of the hypotenuse?F. 222 � x2 � 192 G. 192 � 222 � x2

H. 192 � x2 � 222 I. 192 � 222 � x2 8.

9. The length of one leg of a right triangle is 21 inches and the length ofthe hypotenuse is 35 inches. Find the length of the other leg.A. 12 in. B. 1,268.5 in. C. 28 in. D. 14 in. 9.

10. Which could be the lengths of the sides of a right triangle?F. 18 m, 24 m, 30 m G. 2 cm, 3 cm, 4 cmH. 19 ft, 27 ft, 39 ft I. 56 in., 112 in., 168 in. 10.

11. TELEVISION A 41-foot guy wire is used to brace an antenna. The wire isanchored 9 feet from the base of the antenna. How tall is the antenna?A. 42 ft B. 40 ft C. 80 ft D. 22 ft 11.

12. What is the area of a parallelogram with a base of 6 inches and a heightof 8 inches?F. 96 in2 G. �

34� in2 H. 24 in2 I. 48 in2 12.

13. Find the area of a circle with a diameter of 24 feet. Round to the nearesttenth.A. 1,809.6 ft2 B. 37.7 ft2 C. 452.4 ft2 D. 75.4 ft2 13.

Chapter 11 Test, Form 2A


Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


14.F. 254.5 mm2 G. 28.3 mm2

H. 1,017.9 mm2 I. 56.5 mm2 14.

15.A. 225 m2 B. 360 m2

C. 180 m2 D. 450 m2 15.

16.F. 60 cm2 G. 96 cm2

H. 120 cm2 I. 48 cm2 16.

17.A. 72 m2 B. 108 m2

C. 54 m2 D. 36 m2 17.

18.F. 116.5 in2 G. 50.1 in2

H. 74.1 in2 I. 85.1 in2 18.


19.A. 0.1% B. 13.3%C. 80.0% D. 15.5% 19.

20.

F. 26.7% G. 16%H. 0.3% I. 33.3% 20.


6 in.

8 in.

4 in.

6 m

12 m

9 m

15 cm

9 cm

5 cm 4 cm

12 m15 m

30 m

9 mm

NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 11 Test, Form 2A (continued)



1. Find 112.A. 22 B. 121 C. 13 D. 110 1.

2. Find 302.F. 450 G. 60 H. 300 I. 900 2.

3. Find �196�.A. 14 B. 98 C. 49 D. 16 3.


5. Estimate �102� to the nearest whole number.A. 10 B. 11 C. 12 D. 25 5.


7. Use a calculator to find �173� to the nearest tenth.A. 29,929 B. 13.2 C. 5.6 D. 13.1 7.

8. The lengths of the legs of a right triangle are 16 feet and 30 feet. Whichequation would you solve to find the length of the hypotenuse?F. 162 � x2 � 30 G. 162 � 302 � x2

H. 302 � x2 � 16 I. 302 � 162 � x2 8.

9. The length of one leg of a right triangle is 24 meters, and the length ofthe hypotenuse is 25 meters. Find the length of the other leg.A. 7 m B. 35 m C. 49 m D. 1 m 9.

10. Which could be the lengths of the sides of a right triangle?F. 7 cm, 8 cm, 10 cm G. 20 m, 30 m, 40 mH. 12 ft, 15 ft, 20 ft I. 6 cm, 8 cm, 10 cm 10.

11. TRAVEL The Garcias drove 24 miles east and then 7 miles north. Atthat point, what is the straight-line distance from their starting point?A. 31 mi B. 625 mi C. 312.5 mi D. 25 mi 11.

12. What is the area of a parallelogram with a base of 4 miles and a heightof 8 miles?F. �

12� mi2 G. 32 mi2 H. 16 mi2 I. 64 mi2 12.

13. Find the area of a circle with a radius of 20 yards. Round to the nearest tenth.A. 62.8 yd2 B. 31.4 yd2 C. 314.2 yd2 D. 1,256.6 yd2 13.

Chapter 11 Test, Form 2B


Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


14.F. 10,207.0 m2 G. 179.1 m2

H. 89.5 m2 I. 2,551.8 m2 14.

15.A. 374 cm2 B. 289 cm2

C. 578 cm2 D. 187 cm2 15.

16.F. 735 mm2 G. 367.5 mm2

H. 588 mm2 I. 294 mm2 16.

17.A. 56 m2 B. 40 m2

C. 28 m2 D. 20 m2 17.

18.F. 89.1 mi2 G. 164.5 mi2

H. 105.1 mi2 I. 81.1 mi2 18.


19.A. 3.8% B. 26.3%C. 26.4% D. 0.3% 19.

20.F. 12% G. 40%H. 5% I. 20% 20.


6 cm4 cm

12 cm

8 cm

5 m

8 m

7 m

29 mm

20 mm

15 mm 12 mm

11 cm17 cm

34 cm

57 m

NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 11 Test, Form 2B (continued)


Chapter 11 Test, Form 2C


Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

1. A randomly-dropped counter falls in the squares. Find the 1.probability that it falls in the shaded squares. Write as a percent. Round to the nearest tenth if necessary.

2. CONSTRUCTION A 15-foot ladder is propped against a wall. 2.The base of the ladder is 9 feet from the base of the wall.How far up the wall does the ladder reach?

3. Evaluate a2 � �b� if a � 4 and b � 9. 3.


4. 9 4.

5. 40 5.


6. �144� 6.

7. �1,369� 7.


8. �29� 8.

9. �53� 9.

Use a calculator to find each square root to the nearesttenth.

10. �90� 10.

11. �455� 11.

Find the missing measure of each right triangle. Roundto the nearest tenth if necessary.

12. b � 7 cm, c � 11 cm 12.

Chapter 11 Test, Form 2C (continued)

13. a � 30 ft, c � 50 ft 13.

14. 14.


15. 15.

16. 16.

17. 17.

18. 18.


19. radius � 6 cm 19.

20. 20.

Bonus What is the base of a parallelogram if the height is B:17.5 inches and the area is 245 square inches?

34 in.

16 mi

25 mi

11 mi

15 m

20 m

8 mm14 mm

27 mm

7 ft

8 ft

4 ft

4.3 m

2 m

c m

NAME ________________________________________ DATE ______________ PERIOD _____


Chapter 11 Test, Form 2D

1. A randomly-dropped counter falls in the squares. Find the 1.probability that it falls in the shaded squares. Write as a percent. Round to the nearest tenth if necessary.

2. TRAVEL Sally drives 10 miles east and then 10 miles south. 2.At this point, what is the straight-line distance from her starting point? Estimate to the nearest whole number.



4. 4 4.

5. 30 5.


6. �121� 6.

7. �1,089� 7.


8. �39� 8.

9. �84� 9.


10. �80� 10.

11. �320� 11.

Find the missing measure of each right triangle. Roundto the nearest tenth if necessary.

12. a � 45 m, b � 60 m 12.

13. a � 5 ft, c � 8 ft 13.


Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

14. 14.

Find the area of each figure. Round to the nearest tenthif necessary.

15. 15.

16. 16.

17. 17.

18. 18.


19. diameter � 7 ft 19.

20. 20.

Bonus What is the base of a parallelogram if the height is B:14.5 feet and the area is 174 square feet?

14 in.

42 cm

22 cm

18 cm

4 in.

8 in.

50 mm

25 mm20 mm

6 m4 m

9 m

6.3 cm

x cm

10 cm

NAME ________________________________________ DATE ______________ PERIOD _____

Chapter 11 Test, Form 2D (continued)


Chapter 11 Test, Form 3

1. A randomly-dropped counter falls 1.in the squares. Find the probabilitythat it falls in the shaded squares.Write as a percent. Round to thenearest tenth if necessary.

2. BOATING A 25-foot cable is used to brace 2.a ship mast. The cable is anchored 7 feetfrom the foot of the mast. How tall is the mast?



4. 19 4.

5. 32 5.


6. �441� 6.

7. �256� 7.


8. �84� 8.

9. �141� 9.


10. �68� 10.

11. �932� 11.

Find the missing measure of each right triangle. Round to the nearest tenth if necessary.

12. b � 64 m, c � 80 m 12.

13. a � 11 yd, c � 18 yd 13.

14. 14.

8.7 in.c in.

5 in.


Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Chapter 1 Test, Form 3 (continued)


15. 15.

16. 16.

17. 17.

18. 18.


19. diameter � 100 ft 19.

20. 20.

Bonus What is the height of a parallelogram if the base is B:22 inches and the area is 407 square inches?

19.3 m

57 cm

20 cm

33 cm

6 ft

8 ft

10 ft5 ft

24 m

30 m

25 m

16 cm

10 cm

NAME ________________________________________ DATE ______________ PERIOD _____


Demonstrate your knowledge by giving a clear, concise solution toeach problem. Be sure to include all relevant drawings and justifyyour answers. You may show your solutions in more than one wayor investigate beyond the requirements of the problem. If necessary,record your answer on another piece of paper.

1. a. Explain in your own words what is meant by the square root of anumber.

b. Use a model to show that �17� is about 4.

c. State the Pythagorean Theorem in your own words.

d. Use a right triangle and squares to model 62 � 82 � 102.

e. CARPENTRY A carpenter is framing a house. The front of the house measures 48 feet. The width measures 36 feet. He measures diagonally across the house as shown. If the diagonal measurement is 62 feet, are the corners of the house square (right angles)? Explain your reasoning. Use a calculator.

f. CARPENTRY The carpenter is cutting a brace to keep a window frame square during installation.What is the length of the brace? Explain eachstep. Use a calculator. Round to the nearest tenthif necessary.

2. LANDSCAPING Mrs. Cobel is preparing a bid for sodding a new city park. Her bid is for sodding all of the park except the fountain and garden areas. If she plans to submit a bid for $1.50 per square foot, tell what Mrs. Cobel’s bid will be. Show your work and explain your reasoning. Round to the nearest dollar.

145 ft

300 ft

350 ft

175

ft12

5 ft

fountaingarden

20 ft

30 in.

36 in.

brace

48 ft

36 ft62 ft

Chapter 11 Extended Response Assessment


Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Write whether each sentence is true or false. If false, replacethe underlined term to make a true sentence.

1. To double a number means to multiply that number by itself. 1.

2. An irrational number is a number that cannot be written as 2.a fraction.

3. The diagonal of a rectangle is the leg of a right triangle. 3.

4. A leg is one of the two sides adjacent to the right side of a 4.right triangle.

5. The leg is the side of a right triangle that is opposite the 5.right angle.

6. The height of a parallelogram is the perpendicular distance 6.from the base to the opposite side.

7. A plus sign is the symbol used to indicate the positive square 7.root of a number.

8. A perfect square is the square of a rational number. 8.

9. Two-dimensional figures made up of more than one type of 9.figure are called three-dimensional figures.

10. Square roots are the factors multiplied to form perfect 10.squares.

In your own words, define the term.

11. Pythagorean Theorem

base (p. 483)

complex figure (p. 498)

height (p. 483)

hypotenuse (p. 479)

irrational number (p. 476)

leg (p. 479)

perfect square (p. 471)

Pythagorean Theorem (p. 479)

radical sign (p. 471)

square (p. 470)

square roots (p. 471)

Chapter 11 Vocabulary Test/Review


NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Ass

essm

ent


Find the square of each number. 1.

1. 23 2. 43 3. 36 2.

3.

Find each square root. 4.

4. �36� 5. �361� 6. �676� 5.

6.

Estimate each square root to the nearest whole number. 7.

7. �63� 8. �150� 8.

9. �223� 10. �292� 9.

10.

Find the missing measure of each right triangle. Round to the nearest tenth if necessary.

1. 2. 1.

2.

3. a � 28 mm, c � 35 mm 3.

Find the area of each parallelogram. Round to the nearest tenth if necessary.

4. 5. 4.

5.

39 ft

24 ft17 ft

8.9 m

4.3 m

9 cm12 cm

a cm

48 ft

14 ftc ft

Chapter 11 Quiz(Lessons 11-1 and 11-2)


NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____


Find the area of each figure. 1.

1. 2. 3. 2.

3.

Find the area of each circle. Round to the nearest tenth. 4.

4. radius � 4 in. 5. 5.

3.6 cm

30 ft

20 ft

68 ft

18 ft

65 mm

60 mm80 mm64 m

80 m

120 m


1. 2. 1.

2.


3. 4. 5. 3.

4.

5.

3 in.

4 in.

5 in.5 ft

9 ft




1. Find 92.A. 18 B. 3 C. 81 D. 11 1.

2. Find �144�.F. 12 G. 13 H. 20,736 I. 72 2.

3. Estimate �60� to the nearest whole number.A. 3,600 B. 30 C. 7 D. 8 3.

4. Use a calculator to find �87� to the nearest tenth.F. 9.3 G. 9 H. 43.5 I. 7,569.0 4.

5. Find the missing measure for the triangle.A. 625 m B. 25 mC. 5 m D. 6 m 5.

6. Find the area of the parallelogram.F. 36 in2 G. 18 in2

H. 72 in2 I. 70 in2 6.

Find the square of each number. 7.

7. 9 8. 16 8.

Find each square root. 9.

9. �225� 10. �324� 10.

Estimate each square root to the nearest whole number. 11.

11. �290� 12. �407� 12.

Find the missing measure of each right triangle. Roundto the nearest tenth if necessary. 13.

13. a � 12 cm; c � 13 cm 14. a � 11 m; c � 23 m 14.

15. SKATEBOARDING 15.A skateboarding ramp is4.5 meters long and 2.75 meters tall. To the nearesttenth, how long across the ground is the ramp?

2.75 m4.5 m

12 in.

6 in.

20 m

15 mc m

Chapter 11 Mid-Chapter Test(Lessons 11–1 through 11-4)


Ass

essm

ent

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

1. Simplify 6(�3e). (Lesson 3-6) 1.

2. Write �1350�

in simplest form. (Lesson 5-3) 2.

3. Find 5�58� � 5�

15�. Write in simplest form. (Lesson 6-4) 3.

4. Solve the proportion �n5

� � �3258�

. (Lesson 7-3) 4.

5. Write 13.8% as a fraction in simplest form. (Lesson 7-5) 5.

6. 30 is what percent of 12? (Lesson 8-2) 6.

7. The forecast for Saturday calls for a 45% chance of snow. 7.Describe the complementary event and its probability.(Lesson 9-1)

8. Determine whether a regular decagon can be used by itself 8.to make a tessellation. Explain. (Lesson 10-7)

9. Triangle PQR have vertices P(1, 2), Q(3, 5), and R(6, 0). Find 9.the vertices of P�Q�R� after a translation of 3 units left and 2 units down. Then graph. (Lesson 10-8)

10. Estimate �120� to the nearest whole number. (Lesson 11-2) 10.

11. STUNTS A monster truck attempted to scale a brick wall. 11.The highest point it reached on the wall was 3 meters. At that point, its rear wheels were 4.3 meters from the wall.How long is the monster truck? Round to the nearest hundredth. (Lesson 11-3)

12. Find the area of a triangle with a base measure of 12.10.5 millimeters and a height of 6 millimeters. (Lesson 11-5)

13. Find the area of the circle. Round to the 13.nearest tenth. (Lesson 11-6) 1.5 in.

y

xO

P

Q

R

Chapter 11 Cumulative Review(Chapters 1–11)


NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Ass

essm

ent


1. Evaluate |�8| � |�2|. (Lesson 3-1)

A. �6 B. 10 C. 6 D. �10 1.

2. Write 49.5% as a decimal. (Lesson 5-6)

F. 0.495 G. 4.95 H. 0.0495 I. 4.095 2.

3. Write 0.33% as a decimal. (Lesson 7-6)

A. 0.0033 B. 33 C. 3.3 D. 0.033 3.

4. Find the percent of change from 18 to 41. Round to the nearestwhole percent. (Lesson 8-4)

F. 44% G. 228% H. 56% I. 128% 4.

5. RAFFLE In a raffle, one ticket will be drawn from a total of 200 tickets. If Maureen has 4 tickets, what is the probability that she will win? (Lesson 9-1)

A. �510�

B. �14� C. 0.2 D. 4% 5.

6. HORSES Tionna has a display that holds 8 horse figurines.If she has 17 horse figurines, how many combinations of 8 can she create? (Lesson 9-5)

F. 40,320 G. 136 H. 2,312 I. 24,310 6.

7. Suppose �1 and �2 are complementary. If m�1 � 50º, findm�2. (Lesson 10-3)

A. 30º B. 50º C. 40º D. 130º 7.

8. Three sides of a triangle measure 6 meters, 4 meters, and5 meters. Classify the triangle by its sides. (Lesson 10-4)

F. scalene G. isosceles H. equilateral I. obtuse 8.

9. CABLE A 52-foot cable reaches from the top of a pole to a point on the ground that is 48 feetfrom the base of the pole. How tall is the pole?(Lesson 11-3)

A. 12 ft B. 20 ftC. 92 ft D. 50 ft 9.

10. What is the base of a parallelogram with an area of 30 squaremiles and a height of 5 miles? (Lesson 11-4)

F. 35 mi G. 25 mi H. 152 mi I. 6 mi 10.

11. Find the area of a circle with a diameter of 36 millimeters.Round to the nearest tenth. (Lesson 11-6)

A. 4071.5 mm2 B. 56.5 mm2

C. 113.1 mm2 D. 1017.9 mm2 11. DCBA

IHGF

DCBA

52 ft

48 ft

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

Standardized Test Practice(Chapters 1–11)

Part 1: Multiple Choice

Instructions: Fill in the appropriate oval for the best answer.

12. Order 11, �14, �8, �10, 0, and �3 from least to greatest. 12.(Lesson 3-2)

13. A rectangle has a width of 3.5 inches and 13. 14.a length of 4.25 inches. Find the perimeter of the rectangle in inches. (Lesson 6-8)

14. BAND The ratio of boys to girls in the school band is 2 to 3. If there are 90 students in the band, how many of them are boys?(Lesson 7-3)

15. Use the Fundamental Counting Principle 15.to find the total number of outcomes when choosing a day in the month of September and tossing two coins. (Lesson 9-3) 16.

16. ATHLETICS A rectangular athletic field is 80 meters long by 60 meters wide. What is the diagonal distance across the field in meters? (Lesson 11-3)

17. WINDSTORM A strong storm blew over a billboard 27 feet tall so that it is leaning against a telephone pole 21 feet tall. (Lesson 11-3)

a. Make a drawing to represent this situation.

b. How far from the base of the telephone pole is the base of thebillboard? Round to the nearest tenth if necessary.

Part 3: Extended Response

Instructions: Write your answers below or to the right of the questions.

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

Part 2: Short Response/Grid In

Instructions: Enter your grid in answers by writing each digit of the answer in acolumn box and then shading in the appropriate circle that corresponds to that entry.Write answers to short answer questions in the space provided.

NAME ________________________________________ DATE ______________ PERIOD _____

Standardized Test Practice (continued)

(Chapters 1–11)


An

swer

s

© Glencoe/McGraw-Hill A1 Mathematics: Applications and Concepts, Course 2

Standardized Test PracticeStudent Recording Sheet (Use with pages 508–509 of the Student Edition.)

NAME ________________________________________ DATE ______________ PERIOD _____

SCORE _____

Part 1:

Solve the problem and write your answer in the blank.

For grid in questions, also enter your answer by writing each number or symbolin a box. Then fill in the corresponding circle for that number or symbol.

11. 19.

12.

13.

14.

15.

16.

17.

18.

19. (grid in)

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

Select the best answer from the choices given and fill in the corresponding oval.

Multiple Choice

1.

2.

3.

4.

5.

6.

7.

8.

9.

10. IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

Part 2: Short Response/Grid in

Record your answer for Question 20 on the back of this paper.

Part 3: Extended Response

General Scoring Guidelines• If a student gives only a correct numerical answer to a problem but does not show how he or she

arrived at the answer, the student will be awarded only 1 credit. All extended response questionsrequire the student to show work.

• A fully correct answer for a multiple-part question requires correct responses for all parts of thequestion. For example, if a question has three parts, the correct response to one or two parts of thequestion that required work to be shown is not considered a fully correct response.

• Students who use trial and error to solve a problem must show their method. Merely showing thatthe answer checks or is correct is not considered a complete response for full credit.

Exercise 20 Rubric

Standardized Test PracticeRubric (Use to score the Extended Response question on page 509 of the Student Edition.)

Score Specific Criteria4 The Pythagorean Theorem is used to determine the height of the parallelogram. An

accurate explanation that the area of the side (60 � 46.5 in2) is greater that the areaof the floor (60 � 30 in2) is given. The area of two triangular regions is correctlydetermined to be 1,320 in2.

3 The correct values are found. However, the explanation is correct but not complete.ORThe explanation is correct and complete, but one computational error is made infinding the height of the parallelogram or the area of the two triangular regions.

2 The Pythagorean Theorem is used to determine the height of the parallelogram, andthe explanation is correct and complete. However, the area of only one triangularregion is found. ORThe Pythagorean Theorem is used to determine the height of the parallelogram, thearea of the side is stated to be greater than the area of the floor, and the area of thetwo triangular regions is correctly determined. However, the explanation is incorrector not given.

1 The area of the two triangular regions is correct, but the answer to Part a iscompletely incorrect. ORThe area of the side is stated to be greater than the area of the floor, but theexplanation is incorrect or not given. The area of the two triangular regions isincorrect.

0 Response is completely incorrect.



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4.15

225

5.21

441

6.45

2,02

5

Fin

d e

ach

sq

uar

e ro

ot.

7.�

16 �4

8.�

36�6

9.�

256

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10.

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11.

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484

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NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Sq

uar

es a

nd

Sq

uar

e R

oo

ts

The

pro

duct

of

a nu

mbe

r an

d its

elf

is t

he s

qu

are

of t

he n

umbe

r.N

umbe

rs li

ke 4

, 25

, an

d 2.

25 a

reca

lled

per

fect

sq

uar

esbe

caus

e th

ey a

re s

quar

es o

f ra

tiona

l num

bers

.The

fact

ors

mul

tiplie

d to

form

perf

ect

squa

res

are

calle

d sq

uar

e ro

ots

.Bot

h 5

�5

and

(�5)

(�5)

equ

al 2

5.S

o, 2

5 ha

s tw

o sq

uare

root

s, 5

and

�5.

A r

adic

al s

ign

, �

00 �,

is t

he s

ymbo

l use

d to

indi

cate

the

pos

itive

squa

re r

oot

of a

num

ber.

So,

�25�

�5.

Answers (Lesson 11-1)


©G

lenc

oe/M

cGra

w-H

ill61

2M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Pre-

Act

ivit

yC

om

ple

te t

he

Min

i Lab

at

the

top

of

pag

e 47

0 in

yo

ur

text

bo

ok.

Wri

te y

ou

r an

swer

s b

elo

w.

1.O

n g

rid

pape

r,dr

aw a

nd

labe

l th

ree

oth

er

rect

angl

es t

hat

hav

e a

peri

met

er o

f 16

un

its.

2.S

um

mar

ize

the

dim

ensi

ons

and

area

s of

th

e re

ctan

gles

th

at

you

dre

w i

n a

tab

le l

ike

the

one

show

n b

elow

.

3.D

raw

th

ree

diff

eren

t re

ctan

gles

th

at h

ave

a pe

rim

eter

of

12 u

nit

s an

d fi

nd

thei

r ar

eas.

4.W

hat

do

you

not

ice

abou

t th

e re

ctan

gles

wit

h t

he

grea

test

are

as?

Th

ey a

re s

qu

ares

.

Rea

din

g t

he

Less

on

5a

–c.S

amp

le a

nsw

ers

are

giv

en.

5.In

th

is l

esso

n,t

he

wor

d sq

uar

eis

use

d in

sev

eral

dif

fere

nt

way

s.T

ell

the

mea

nin

g of

th

e w

ord

as i

t is

use

d in

eac

h p

hra

se o

r se

nte

nce

.a.

Fin

d th

e sq

uar

eof

3.

3 ti

mes

3b

.9 u

nit

s sq

uar

ed9

squ

are

un

its;

9 sq

uar

es w

ith

sid

es o

f 1

un

it e

ach

c.A

box

ing

rin

g is

a s

quar

ew

ith

an

are

a of

400

ft2

.a

rect

ang

le w

ith

eq

ual

sid

es

Hel

pin

g Y

ou

Rem

emb

er6.

Wor

k w

ith

a p

artn

er.U

se a

cal

cula

tor

to f

ind

the

squ

ares

of

six

nu

mbe

rs,

som

e of

th

em d

ecim

als.

Th

en w

rite

on

ly t

he

squ

ares

in

a l

ist

and

exch

ange

lis

ts w

ith

you

r pa

rtn

er.F

ind

the

squ

are

root

s of

th

e sq

uar

es i

nth

e li

st t

hat

you

rec

eive

.Wri

te y

our

answ

ers

in t

he

form

�x �

�y.

See

stu

den

ts’w

ork

.

5 un

its1

unit

4 un

its2

units

3 un

its

3 un

its

5 sq

uare

uni

ts8

squa

re u

nits

9 sq

uare

uni

ts

2 �

612 16

3 �

5

4 �

4

15

1 �

77

Dra

win

gD

imen

sio

ns

(un

its)

A

rea

(sq

un

its)

6 un

its

2 un

its

5 un

its

3 un

its

4 un

its

4 un

its

Read

ing

to L

earn

Mat

hem

atic

sS

qu

ares

an

d S

qu

are

Ro

ots

©G

lenc

oe/M

cGra

w-H

ill61

1M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice:

Wor

d Pr

oble

ms

Sq

uar

es a

nd

Sq

uar

e R

oo

ts

Lesson 11–1

1.FE

RTI

LIZE

RJo

hn

bou

ght

a ba

g of

law

nfe

rtil

izer

th

at w

ill

cove

r 40

0 sq

uar

efe

et.W

hat

are

th

e di

men

sion

s of

th

ela

rges

t sq

uar

e pl

ot o

f la

wn

th

at t

he

bag

of f

erti

lize

r w

ill

cove

r?20

ft

by 2

0 ft

2.G

EOM

ETRY

Th

e ar

ea A

of

a ci

rcle

in

squ

are

feet

wit

h a

rad

ius

r in

fee

t is

give

n a

ppro

xim

atel

y by

th

e fo

rmu

laA

�3.

14r2

.Wh

at i

s th

e ap

prox

imat

ear

ea o

f a

circ

le w

ith

a r

adiu

s of

3 f

eet?

28.2

6 ft

2

3.M

OTI

ON

Th

e ti

me

tin

sec

onds

for

an

obje

ct d

ropp

ed f

rom

a h

eigh

t of

hfe

etto

hit

th

e gr

oun

d is

giv

en b

y th

e

form

ula

t�

��2 3h 2� �.H

ow l

ong

wil

l it

tak

e

an o

bjec

t dr

oppe

d fr

om a

hei

ght

of

500

feet

to

hit

th

e gr

oun

d? R

oun

d to

the

nea

rest

ten

th.

5.6

s

4.PA

CK

AG

ING

A c

ardb

oard

en

velo

pe f

or a

com

pact

dis

c is

a s

quar

e w

ith

an

are

aof

171

.61

squ

are

cen

tim

eter

s.W

hat

are

the

dim

ensi

ons

of t

he

enve

lope

?13

.1 c

m b

y 13

.1 c

m

5.G

EOG

RA

PHY

Ref

er t

o th

e sq

uar

esbe

low

.Th

ey r

epre

sen

t th

e ap

prox

imat

ear

eas

of C

alif

orn

ia,A

laba

ma,

and

Neb

rask

a.F

ind

the

area

of A

laba

ma.

50,6

25 m

i2

277

mi

225

mi

395

mi

ALNE

CA

6.U

se t

he

figu

re i

n E

xerc

ise

5.H

ow m

uch

larg

er i

s C

alif

orn

ia t

han

Neb

rask

a?79

,296

mi2



An

swer

s

©G

lenc

oe/M

cGra

w-H

ill61

4M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Est

imat

e �

40�to

th

e n

eare

st w

hol

e n

um

ber

.

Lis

t so

me

perf

ect

squ

ares

.

1,4,

9,16

,25,

36,4

9,…

36�

40

�49

40 is

bet

wee

n th

e pe

rfec

t sq

uare

s 36

and

49.

�36�

��

40��

�49�

Fin

d th

e sq

uare

roo

t of

eac

h nu

mbe

r.

6�

�40�

�7

�36�

�6

and

�49�

�7

So,

�40�

is b

etw

een

6 a

nd

7.S

ince

40

is c

lose

r to

36

than

to

49,t

he

best

wh

ole

nu

mbe

res

tim

ate

is 6

.

Use

a c

alcu

lato

r to

fin

d t

he

valu

e of

�28 �

toth

e n

eare

st t

enth

.

285.

2915

0262

2

�28�

�5.

3

Ch

eck

Sin

ce 5

2�

25 a

nd

25 i

s cl

ose

to 2

8,th

e an

swer

is

reas

onab

le.

Est

imat

e ea

ch s

qu

are

root

to

the

nea

rest

wh

ole

nu

mb

er.

1.�

3�2

2.�

8�3

3.�

26�5

4.�

41�6

5.�

61�8

6.�

94�10

7.�

152

�12

8.�

850

�29

Use

a c

alcu

lato

r to

fin

d e

ach

sq

uar

e ro

ot t

o th

e n

eare

st t

enth

.

9.�

2�1.

410

.�

27�5.

2

11.

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12.

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13.

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10.2

14.

�39

5�

19.9

15.

�84

6�

29.1

16.

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298

�47

.9

ENTE

R2n

d

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Est

imat

ing

Sq

uar

e R

oo

ts

Rec

all t

hat

a pe

rfec

t sq

uare

is a

squ

are

of a

rat

iona

l num

ber.

In L

esso

n 5-

8, y

ou le

arne

d th

at a

nynu

mbe

r th

at c

an b

e w

ritte

n as

a f

ract

ion

is a

rat

iona

l num

ber.

A n

umbe

r th

at c

anno

t be

writ

ten

as a

frac

tion

is a

n ir

rati

on

al n

um

ber

.

01

23

45

6

28

©G

lenc

oe/M

cGra

w-H

ill61

3M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

The

Geo

met

ric

Mea

nT

he

squ

are

root

of

the

prod

uct

of

two

nu

mbe

rs i

s ca

lled

th

eir

geom

etri

c m

ean

.T

he

geom

etri

c m

ean

of

12 a

nd

48 i

s �

12�

4�

8��

�57

6�

or 2

4.

Fin

d t

he

geom

etri

c m

ean

for

eac

h p

air

of n

um

ber

s.

1.2

and

84

2.4

and

96

3.9

and

1612

4.16

an

d 4

85.

16 a

nd

3624

6.12

an

d 3

6

7.18

an

d 8

128.

2 an

d 18

69.

27 a

nd

1218

Rec

all

the

defi

nit

ion

of

a ge

omet

ric

seq

uen

ce.E

ach

ter

m i

s fo

un

d by

mu

ltip

lyin

g th

e pr

evio

us

term

by

the

sam

e n

um

ber.

A m

issi

ng

term

in

age

omet

ric

sequ

ence

equ

als

the

geom

etri

c m

ean

of

the

two

term

s on

eit

her

side

.

Fin

d t

he

mis

sin

g te

rm i

n e

ach

geo

met

ric

seq

uen

ce.

10.

4,12

,,1

08,3

2436

11.

10,

,62.

5,15

6.25

,390

.625

25

12.

1,0.

4,,0

.064

,0.0

256

0.16

13.

700,

70,7

,0.7

,,0

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0.07

14.

6,,2

412

15.

18,

,32

24?

?

??

??En

richm

ent

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enric

hmen

t

Lesson 11–1

Answers (Lessons 11-1 and 11-2)


NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice:

Wor

d Pr

oble

ms

Est

imat

ing

Sq

uar

e R

oo

ts

©G

lenc

oe/M

cGra

w-H

ill61

6M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

1.G

EOM

ETRY

Th

e di

amet

er d

of a

cir

cle

wit

h a

rea

Ais

giv

en b

y th

e fo

rmu

la

d�

��4 �A � �.W

hat

is

the

diam

eter

of

a

circ

le w

ith

an

are

a of

56

squ

are

inch

es?

Use

3.1

4 fo

r �

and

rou

nd

to t

he

nea

rest

ten

th.

8.4

in.

2.FE

NC

ING

Car

men

wan

ts t

o bu

y fe

nci

ng

to e

ncl

ose

a sq

uar

e ga

rden

wit

h a

nar

ea o

f 50

0 sq

uar

e fe

et.H

ow m

uch

fen

cin

g do

es C

arm

en n

eed

to b

uy?

Rou

nd

to t

he

nea

rest

ten

th.

89.4

ft

3.O

CEA

NS

Th

e sp

eed

vin

fee

t pe

r se

con

dof

an

oce

an w

ave

in s

hal

low

wat

er o

fde

pth

din

fee

t is

giv

en b

y th

e fo

rmu

lav

��

32d

�.W

hat

is

the

spee

d of

an

ocea

n w

ave

at a

dep

th o

f 10

fee

t?R

oun

d to

th

e n

eare

st t

enth

.17

.9 f

t/s

4.LI

GH

TIN

GA

new

fla

shli

ght

has

a b

eam

wh

ose

wid

th w

at a

dis

tan

ce d

from

th

efl

ash

ligh

t is

giv

en b

y th

e fo

rmu

law

�1.

2�d �.

Wh

at i

s th

e w

idth

of

the

beam

at

a di

stan

ce o

f 30

fee

t? R

oun

d to

the

nea

rest

ten

th.

6.6

ft

5.SO

UN

DT

he

spee

d of

sou

nd

in a

ir c

inm

eter

s pe

r se

con

d at

a t

empe

ratu

re T

in d

egre

es C

elsi

us

is g

iven

appr

oxim

atel

y by

th

e fo

rmu

la

c�

�40

2(T

��

273

�)�.

Wh

at i

s th

e sp

eed

of s

oun

d in

air

at

a te

mpe

ratu

re o

f 25

deg

rees

Cel

siu

s? R

oun

d to

th

en

eare

st t

enth

.34

6.1

m/s

6.PR

OJE

CTI

LES

Th

e m

uzz

le v

eloc

ity

vin

feet

per

sec

ond

nec

essa

ry f

or a

can

non

to h

it a

tar

get

xfe

et a

way

is

esti

mat

edby

th

e fo

rmu

la v

��

32x

�.W

hat

mu

zzle

velo

city

is

requ

ired

to

hit

a t

arge

t3,

000

feet

aw

ay?

Rou

nd

to t

he

nea

rest

ten

th.

309.

8 ft

/s

3,00

0 ft

Lesson 11–2

©G

lenc

oe/M

cGra

w-H

ill61

5M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Est

imat

e ea

ch s

qu

are

root

to

the

nea

rest

wh

ole

nu

mb

er.

1.�

5 �2

2.�

10�3

3.�

21�5

4.�

28�5

5.�

78�9

6.�

102

�10

7.�

179

�13

8.�

274

�17

9.�

303

�17

10.

�56

3�

2411

.�

592

�24

12.

�75

5�

27

13.

�98

1�

3114

.�

1,35

6�

3715

.�

1,68

8�

41

16.

�3,

287

�57

17.

�3,

985

�63

18.

�4,

125

�64

Use

a c

alcu

lato

r to

fin

d e

ach

sq

uar

e ro

ot t

o th

e n

eare

st t

enth

.

19.

�6 �

2.4

20.

�19�

4.4

21.

�30�

5.5

22.

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8.8

23.

�11

4�

10.7

24.

�12

5�

11.2

25.

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9�

12.2

26.

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2�

13.5

27.

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14.6

28.

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6�

20.9

29.

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1�

24.9

30.

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29.2

31.

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8�

30.3

32.

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004

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.733

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1,27

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35.6

34.

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438

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64.9

36.

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786

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37.

Ord

er �2 75 �

,4.9

1,an

d �

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om l

east

to

grea

test

.�2 75 �

,�23�

,4.9

1

38.

Gra

ph �

42�an

d �

62�on

th

e sa

me

nu

mbe

r li

ne.

01

23

45

87

64262

Prac

tice:

Ski

llsE

stim

atin

g S

qu

are

Ro

ots

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

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Stud

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and

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rven

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Th

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right

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c2�

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leng

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ac



An

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Pre-

Act

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th

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tro

du

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p o

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age

479

in y

ou

r te

xtb

oo

k.W

rite

yo

ur

answ

ers

bel

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.

1.C

an t

he

mir

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mo

re t

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7 f

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op

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u k

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diag

onal

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oten

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on p

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Th

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Lesson 11–3

1.O

RIG

AM

IC

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has

a p

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.0 in

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2.C

OM

PUTE

RS

In a

com

pute

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3.A

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he

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e is

anch

ored

to

the

grou

nd

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ove

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nd.

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at i

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the

pole

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her

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4 m

9 m

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PSC

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ants

to

buil

d a

ram

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ill

rise

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ong

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l th

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nd

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nea

rest

ten

th.

20.4

ft

4 ft

20 ft

x ft

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OLS

Sal

omon

sw

ims

diag

onal

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ross

his

poo

l ev

ery

day.

If S

alom

on’s

pool

is

4 m

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ide

and

16 m

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agon

ally

acr

oss,

how

lon

g is

his

poo

l,to

th

e n

eare

st t

enth

of

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.5 m

6.FR

AM

ESR

osa

has

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e th

atm

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12 i

nch

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y 18

in

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.Wh

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th

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th

e n

eare

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.21

.6 in

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mat

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App

licat

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Con

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s, C

ours

e 2

Fin

d t

he

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if

the

bas

e

is 6

in

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ght

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____

____

____

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____

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of a

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hei

ght

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gmen

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mat

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s, C

ours

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Pyth

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Air

In t

he

diag

ram

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the

righ

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air

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0 m

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t,th

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airp

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lly

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f n

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e m

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in

th

edi

agra

m s

how

s th

e ac

tual

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ecti

on o

f th

e ai

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Th

e ac

tual

spe

ed o

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d o

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e.R

oun

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nea

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th.(

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els

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____

____

____

____

____

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s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

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IOD

__

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Prac

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Are

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mat

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App

licat

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s, C

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1.SA

ILS

Joyc

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licat

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cept

s, C

ours

e 2

Fin

d t

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area

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each

par

alle

logr

am.R

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o th

e n

eare

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enth

if

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essa

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ft2

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ME

____

____

____

____

____

____

____

____

____

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DAT

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____

____

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ER

IOD

__

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Two

Are

a Pu

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five

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ME

____

____

____

____

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____

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____

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mat

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licat

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ours

e 2

2 in

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1 in

.

1 in

.

2 in

.

2 in

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mat

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licat

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and

Con

cept

s, C

ours

e 2

Pre-

Act

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yC

om

ple

te t

he

Min

i Lab

at

the

top

of

pag

e 48

3 in

yo

ur

text

bo

ok.

Wri

te y

ou

r an

swer

s b

elo

w.

1.W

hat

is

the

valu

e of

xan

d y

for

each

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x�

4 u

nit

s,y

�2

un

its

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t th

e gr

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quar

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o fi

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area

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each

par

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8 sq

un

its

3.O

n g

rid

pape

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hre

e di

ffer

ent

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in w

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its

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ind

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area

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.

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e ar

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20

sq u

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e a

con

ject

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abou

t h

ow t

o fi

nd

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area

of

a pa

rall

elog

ram

if

you

know

th

e va

lues

of

xan

d y.

Th

e ar

ea e

qu

als

x�

y.

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din

g t

he

Less

on

5.E

xpla

in h

ow t

o fi

nd

the

hei

ght

of a

par

alle

logr

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ple

an

swer

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raw

ase

gm

ent

per

pen

dic

ula

r to

th

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ase

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nd

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ints

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op

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site

sid

es o

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e p

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m.T

he

hei

gh

t is

th

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ng

th o

f th

is s

egm

ent.

6.S

upp

ose

you

are

ask

ed t

o fi

nd

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area

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para

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elow

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give

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xpla

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he

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amp

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nsw

er:T

he

area

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fo

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d u

sin

g t

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len

gth

of

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sid

e o

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ep

aral

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m in

stea

d o

f th

e h

eig

ht.

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e co

rrec

t an

swer

is 3

6 cm

2 .

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pin

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ou

Rem

emb

er7.

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ause

rec

tan

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,rh

ombu

ses,

and

squ

ares

are

all

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the

form

ula

for

fin

din

g th

e ar

ea o

f a

para

llel

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m i

s al

so u

sed

to f

ind

the

area

s of

eac

h o

f th

ese

figu

res.

Th

ink

of a

way

to

rem

embe

r th

at t

he

area

of a

par

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logr

am i

s th

e pr

odu

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s ba

se a

nd

hei

ght.

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exa

mpl

e,dr

aw s

ever

al p

aral

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gram

s,re

ctan

gles

,rh

ombu

ses,

and

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an

dla

bel

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base

an

d h

eigh

t fo

r ea

ch.W

rite

th

e fo

rmu

la f

or t

he

area

bel

owea

ch m

odel

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ee s

tud

ents

’wo

rk.

3 cm

5 cm

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m

4 51

squ

are

= 1

ft

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squ

are

= 1

ft

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squ

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hem

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rea

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ram

s

NA

ME

____

____

____

____

____

____

____

____

____

____

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E _

____

____

____

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ER

IOD

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Lesson 11–4



An

swer

s

Fin

d t

he

area

of

each

fig

ure

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nd

to

the

nea

rest

ten

th i

f n

eces

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.

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cm

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3 ft

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tria

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tria

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m

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NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

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ER

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Prac

tice:

Ski

llsA

rea

of T

rian

gle

s an

d T

rap

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ids

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mat

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licat

ions

and

Con

cept

s, C

ours

e 2

Lesson 11–5

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lenc

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athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Fin

d t

he

area

of

the

tria

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e.E

stim

ate

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a of

a t

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lace

bw

ith 6

and

hw

ith 4

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13.5

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tiply

.

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e ar

ea o

f th

e tr

ian

gle

is 1

3.5

squ

are

inch

es.T

his

is c

lose

to

the

estim

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d t

he

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the

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met

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d t

he

area

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ure

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nd

to

the

nea

rest

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th i

f n

eces

sary

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3.4.

42 f

t231

.5 m

m2

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in2

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5 cm

2

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14 in

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7 m

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m12

ft7 ft

4 cm

3 cm

6 cm

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6 in

.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Are

a o

f Tri

ang

les

and

Tra

pez

oid

s

The

are

a A

of a

tria

ngle

equ

als

half

the

prod

uct

of it

s ba

se b

and

its h

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A�

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tw

o ba

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he h

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a t

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he

dist

ance

bet

wee

n th

e tw

o ba

ses.

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are

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of a

tra

pezo

id e

qual

s ha

lf th

e pr

oduc

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hei

ght

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d th

e su

m o

f th

e ba

ses

b 1an

d b 2

.

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1�

b 2)

b 1 b 2

h

The

base

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trian

gle

can

bean

y of

its

side

s.

The

heig

ht is

the

dist

ance

from

a b

ase

to th

e op

posi

te v

erte

x.

b

h



Pre-

Act

ivit

yC

om

ple

te t

he

Min

i Lab

at

the

top

of

pag

e 48

9 in

yo

ur

text

bo

ok.

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te y

ou

r an

swer

s b

elo

w.

1.W

hat

is

the

area

of

the

para

llel

ogra

m?

24 s

q u

nit

s

2.C

ut

alon

g th

e di

agon

al.W

hat

is

tru

e ab

out

the

tria

ngl

es f

orm

ed?

Th

eyar

e co

ng

ruen

t.

3.W

hat

is

the

area

of

each

tri

angl

e?12

sq

un

its

4.If

th

e ar

ea o

f a

para

llel

ogra

m i

s bh

,th

en w

rite

an

exp

ress

ion

for

th

e ar

eaA

of e

ach

of

the

two

con

gru

ent

tria

ngl

es t

hat

for

m t

he

para

llel

ogra

m.

A =

�1 2�bh

Rea

din

g t

he

Less

on

5.In

a t

rian

gle,

wh

ich

sid

e is

th

e ba

se?

Sam

ple

an

swer

:Th

e b

ase

can

be

any

sid

e o

f th

e tr

ian

gle

.

6.H

ow d

o yo

u f

ind

the

hei

ght

of a

tri

angl

e?S

amp

le a

nsw

er:

On

ceyo

u k

no

w w

hic

h s

ide

is t

he

bas

e,fi

nd

th

e d

ista

nce

fro

m t

he

bas

e to

th

e o

pp

osi

te v

erte

x.

7.F

or w

hat

kin

d of

tri

angl

e m

igh

t th

e h

eigh

t be

fou

nd

outs

ide

of t

he

tria

ngl

e?o

btu

se t

rian

gle

8.H

ow i

s th

e h

eigh

t of

a t

rape

zoid

sim

ilar

to

the

hei

ght

of a

tri

angl

e or

para

llel

ogra

m?

Sam

ple

an

swer

:It

is p

erp

end

icu

lar

to t

he

bas

e.

Hel

pin

g Y

ou

Rem

emb

er9.

Th

e M

ini

Lab

in

th

is l

esso

n g

ave

you

a g

ood

way

to

rem

embe

r th

efo

rmu

la f

or t

he

area

of

a tr

ian

gle

by s

how

ing

you

th

at i

t is

hal

f th

e ar

eaof

a p

aral

lelo

gram

,so

A�

�1 2�bh

.Th

ink

of a

way

to

hel

p yo

u r

emem

ber

the

form

ula

for

th

e ar

ea o

f a

trap

ezoi

d.D

o yo

u r

ecog

niz

e an

yth

ing

in t

he

form

ula

A�

�1 2�h(b

1�

b 2)?

Sam

ple

an

swer

:F

ind

ing

�1 2�(b

1�

b2)

mea

ns

to f

ind

th

e av

erag

e o

f th

e le

ng

ths

of

the

bas

es.S

o,

the

area

of

a tr

apez

oid

is t

he

pro

du

ct o

f th

e av

erag

e o

f th

ele

ng

ths

of

the

bas

es t

imes

th

e h

eig

ht.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Read

ing

to L

earn

Mat

hem

atic

sA

rea

of T

rian

gle

s an

d T

rap

ezo

ids

©G

lenc

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cGra

w-H

ill63

2M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

©G

lenc

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cGra

w-H

ill63

1M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Prac

tice:

Wor

d Pr

oble

ms

Are

a o

f Tri

ang

les

and

Tra

pez

oid

s

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Lesson 11–5

1.G

EOG

RA

PHY

Ark

ansa

s h

as a

sh

ape

that

is s

imil

ar t

o a

trap

ezoi

d w

ith

bas

es o

fab

out

182

mil

es a

nd

267

mil

es a

nd

ah

eigh

t of

abo

ut

254

mil

es.E

stim

ate

the

area

of

the

stat

e.57

,023

mi2

2.PA

TIO

SG

reta

is

mak

ing

a pa

tio

wit

hth

e di

men

sion

s gi

ven

in

th

e fi

gure

.W

hat

is

the

area

of

the

pati

o?

172.

5 ft

215 ft

15 ft

8 ft

3.FL

AG

SM

alil

a w

ants

to

mak

e th

eIn

tern

atio

nal

Mar

ine

Sig

nal

fla

g sh

own

wh

ich

rep

rese

nts

th

e n

um

ber

six.

Wh

atis

th

e ar

ea o

f th

e fl

ag?

1,75

0 in

2

30 in

.10

0 in

.5

in.

4.SI

GN

SE

stim

ate

the

area

of

the

yiel

dsi

gn.

390

in2

30 in

.

26 in

.

5.TI

LIN

GA

cer

amic

s co

mpa

ny

wan

ts t

opr

odu

ce t

iles

in

th

e sh

ape

show

n.W

hat

is t

he

area

of

the

surf

ace

of e

ach

til

e?

36.1

25 c

m2

8.5

cm

8.5

cm

6.G

AR

DEN

ING

Kin

u w

ants

to

buy

tops

oil

for

a se

ctio

n o

f h

er g

arde

n t

hat

has

th

edi

men

sion

s sh

own

in

th

e fi

gure

.Wh

atis

th

e ar

ea o

f th

is s

ecti

on o

f K

inu

’sga

rden

?

7 yd

2

4 yd

3.5

yd 4 yd



An

swer

s

©G

lenc

oe/M

cGra

w-H

ill63

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athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Fin

d t

he

area

of

the

circ

le.

A�

�r2

Are

a of

circ

le

A�

��

52R

epla

ce r

with

5.

578

.539

8163

4

Th

e ar

ea o

f th

e ci

rcle

is

appr

oxim

atel

y 78

.5 s

quar

e ce

nti

met

ers.

Fin

d t

he

area

of

a ci

rcle

th

at h

as a

dia

met

er o

f 9.

4 m

illi

met

ers.

A�

�r2

Are

a of

a c

ircle

A�

��

4.72

Rep

lace

rw

ith 9

.4

2 or

4.7

.

A�

69.4

Use

a c

alcu

lato

r.

Th

e ar

ea o

f th

e ci

rcle

is

appr

oxim

atel

y 69

.4 s

quar

e m

illi

met

ers.

Fin

d t

he

area

of

each

cir

cle.

Rou

nd

to

the

nea

rest

ten

th.

1.2.

3.

153.

9 in

249

0.9

mm

245

2.4

ft2

4.ra

diu

s �

2.6

cm5.

radi

us

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.3 i

n.

6.di

amet

er �

5 �1 2�

yd

21.2

cm

264

2.4

in2

23.8

yd

2

7.di

amet

er �

4�3 4�

mi

8.di

amet

er �

7.9

mm

9.ra

diu

s �

2 �1 5�

ft

17.7

mi2

49.0

mm

215

.2 f

t2

12 ft

25 m

m7

in.

ENTE

R�

�

5 c

m

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Stud

y Gu

ide

and

Inte

rven

tion

Are

a o

f C

ircl

es

The

are

a A

of a

circ

le e

qual

s th

e pr

oduc

t of

pi (

�)

and

the

squa

re o

f its

rad

ius

r.

A�

�r2

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lenc

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ill63

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athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Her

on

’s F

orm

ula

A f

orm

ula

nam

ed a

fter

Her

on o

f Ale

xan

dria

,Egy

pt,c

an b

e u

sed

to f

ind

the

area

of

a tr

ian

gle

give

n t

he

len

gth

s of

its

sid

es.

Her

on’s

for

mu

last

ates

th

at t

he

area

Aof

a t

rian

gle

wh

ose

side

s m

easu

rea,

b,an

d c

is g

iven

by

A�

�s(

s�a

�)(

s�b)

�(s

�c)

�,

wh

ere

sis

th

e se

mip

erim

eter

:

s�

�a�

2b�

c�

.

1–6

Est

imat

es w

ill v

ary.

Est

imat

e th

e ar

ea o

f ea

ch t

rian

gle

by

fin

din

g th

e m

ean

of

the

inn

eran

d o

ute

r m

easu

res.

Th

en u

se H

eron

’s F

orm

ula

to

com

pu

te a

mor

eex

act

area

.Giv

e ea

ch a

nsw

er t

o th

e n

eare

st t

enth

of

a sq

uar

e u

nit

.

1.2.

3.

Est

imat

ed a

rea:

15E

stim

ated

are

a:38

Est

imat

ed a

rea:

25

Com

pute

d ar

ea:

15.6

Com

pute

d ar

ea:

37.4

Com

pute

d ar

ea:

24

4.5.

6.

Est

imat

ed a

rea:

20.5

Est

imat

ed a

rea:

12.5

Est

imat

ed a

rea:

18

Com

pute

d ar

ea:

21.2

Com

pute

d ar

ea:

11.8

Com

pute

d ar

ea:

17.4

9

57

8

83

7 77

6

8

109

9

106

66

Enric

hmen

tN

AM

E__

____

____

____

____

____

____

____

____

____

__D

ATE

___

____

____

___

PE

RIO

D

____

_

Lesson 11–5



NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Prac

tice:

Wor

d Pr

oble

ms

Are

a o

f C

ircl

es

©G

lenc

oe/M

cGra

w-H

ill63

6M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

1.PO

OLS

Su

san

des

ign

ed a

cir

cula

r po

olw

ith

a d

iam

eter

of

25 m

eter

s.W

hat

is

the

area

of

the

bott

om o

f th

e po

ol?

Rou

nd

to t

he

nea

rest

ten

th.

490.

9 m

2

2.M

ON

EYF

ind

the

area

of

the

coin

to

the

nea

rest

ten

th.

283.

5 m

m2

19 m

m

3.D

RU

MS

Wh

at i

s th

e ar

ea o

f th

edr

um

hea

d on

th

e dr

um

sh

own

bel

ow?

Rou

nd

to t

he

nea

rest

ten

th.

153.

9 in

214 in

.

4.PI

ZZA

Est

imat

e th

e ar

ea o

f th

e to

p of

aro

un

d pi

zza

that

has

a d

iam

eter

of

16 i

nch

es.R

oun

d to

th

e n

eare

st t

enth

.20

1.1

in2

5.G

AR

DEN

ING

Jan

e n

eeds

to

buy

mu

lch

for

the

gard

en w

ith

th

e di

men

sion

ssh

own

in

th

e fi

gure

.For

how

mu

ch a

rea

does

Jan

e n

eed

to b

uy

mu

lch

? R

oun

d to

the

nea

rest

ten

th. 95

.0 y

d2

5.5

yd

6.U

TILI

TIES

Wh

at i

s th

e ar

ea o

f th

e to

psu

rfac

e of

a c

ircu

lar

man

hol

e co

ver

that

has

a r

adiu

s of

30

cen

tim

eter

s? R

oun

dto

th

e n

eare

st t

enth

.2,

827.

4 cm

2Lesson 11–6

©G

lenc

oe/M

cGra

w-H

ill63

5M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Fin

d t

he

area

of

each

cir

cle.

Rou

nd

to

the

nea

rest

ten

th.

1.3.

1 cm

22.

12.6

yd

2

3.96

2.1

mm

24.

615.

8 in

2

5.14

.5 f

t26.

50.3

cm

2

7.69

.4 y

d2

8.1,

590.

4 in

2

9.3.

5 m

m2

10.

444.

9 ft

2

11.

radi

us

�5.

7 m

m12

.ra

diu

s �

8.2

ft10

2.1

mm

221

1.2

ft2

13.

diam

eter

�3 �

1 4�in

.14

.di

amet

er �

15.6

cm

8.3

in2

191.

1 cm

2

15.

radi

us

�1.

1 in

.16

.di

amet

er �

12�3 4�

yd3.

8 in

212

7.7

yd2

11.9

ft2.

1 m

m

22.5

in.

4.7

yd

8 cm

4.3

ft

14 in

.35

mm

4 yd

1 cm

Prac

tice:

Ski

llsA

rea

of

Cir

cles

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___



An

swer

s

Seki

Ko

wa

Japa

nes

e m

ath

emat

icia

n S

eki

Kow

a (c

.164

2–17

08)

is c

alle

d T

he

Ari

thm

etic

al S

age

beca

use

of

his

man

y co

ntr

ibu

tion

s to

th

e de

velo

pmen

t of

mat

hem

atic

s in

Jap

an.B

efor

e S

eki,

mat

hem

atic

s in

Jap

an w

as

con

side

red

a fo

rm o

f ar

t to

be

enjo

yed

by i

nte

llec

tual

s in

th

eir

leis

ure

ti

me.

Sek

i de

mon

stra

ted

the

prac

tica

l u

ses

of m

ath

emat

ics

and

intr

odu

ced

soci

al r

efor

ms

that

mad

e it

pos

sibl

e fo

r an

yon

e,n

ot ju

st

inte

llec

tual

s,to

stu

dy m

ath

emat

ics.

On

e of

Sek

i’s c

ontr

ibu

tion

s to

mat

hem

atic

s w

as h

is c

alcu

lati

on o

f a

valu

eof

�th

at w

as c

orre

ct t

o ei

ghte

en d

ecim

al p

lace

s.

��

3.14

1592

6535

8979

3238

…

Sek

i h

ad n

otic

ed t

he

phen

omen

on t

hat

you

see

at

the

righ

t:as

th

en

um

ber

of s

ides

of

a re

gula

r po

lygo

n i

ncr

ease

s,th

e po

lygo

n l

ooks

mor

e an

d m

ore

like

a c

ircl

e.S

o,S

eki

calc

ula

ted

the

foll

owin

g ra

tio

for

poly

gon

s of

in

crea

sin

gly

man

y si

des.

As

the

nu

mbe

r of

sid

es o

f th

e po

lygo

n g

ets

larg

er,t

his

rat

io m

ust

get

clos

er t

o th

e ra

tio

of t

he

circ

um

fere

nce

of

the

circ

le t

o th

e di

amet

er o

fth

e ci

rcle

.Th

is r

atio

,of

cou

rse,

is �

.

You

are

giv

en i

nfo

rmat

ion

bel

ow a

bou

t a

regu

lar

pol

ygon

an

d t

he

circ

le d

raw

n a

rou

nd

th

e p

olyg

on.U

se a

cal

cula

tor

to f

ind

Sek

i’sra

tio.

(Giv

e as

man

y d

ecim

al p

lace

s as

th

ere

are

in y

our

calc

ula

tor

dis

pla

y.)

Wh

at d

o yo

u n

otic

e ab

out

you

r an

swer

s?

1.le

ngt

h o

f on

e si

de �

52.

len

gth

of

one

side

�4.

5922

nu

mbe

r of

sid

es �

6n

um

ber

of s

ides

�8

diam

eter

of

circ

le �

10di

amet

er o

f ci

rcle

�12

33.

0614

6666

7

3.le

ngt

h o

f on

e si

de �

3.75

444.

len

gth

of

one

side

�37

.544

3n

um

ber

of s

ides

�20

nu

mbe

r of

sid

es �

20di

amet

er o

f ci

rcle

�24

diam

eter

of

circ

le �

240

3.12

8666

667

3.12

8691

667

5.le

ngt

h o

f on

e si

de �

1.67

546.

len

gth

of

one

side

�2.

6389

nu

mbe

r of

sid

es �

150

nu

mbe

r of

sid

es �

500

diam

eter

of

circ

le �

80di

amet

er o

f ci

rcle

�42

03.

1413

753.

1415

4761

9A

s th

e n

um

ber

of

sid

es in

crea

ses,

the

rati

o g

ets

clo

ser

to t

he

valu

e o

f �

giv

en a

bov

e.

peri

met

er o

f re

gula

r po

lygo

n�

��

��

�di

amet

er o

f ci

rcle

dra

wn

aro

un

d th

e po

lygo

n

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Enric

hmen

t

©G

lenc

oe/M

cGra

w-H

ill63

8M

athe

mat

ics:

App

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s, C

ours

e 2

Pre-

Act

ivit

yC

om

ple

te t

he

Min

i Lab

at

the

top

of

pag

e 49

3 in

yo

ur

text

bo

ok.

Wri

te y

ou

r an

swer

s b

elo

w.

1.W

hat

is

the

mea

sure

men

t of

th

e ba

se a

nd

the

hei

ght?

�1 2�C;

r

2.S

ubs

titu

te t

hes

e va

lues

in

to t

he

form

ula

for

th

e ar

ea o

f a

para

llel

ogra

m.

A�

�1 2�C(r

)

3.R

epla

ce C

wit

h t

he

expr

essi

on f

or t

he

circ

um

fere

nce

of

a ci

rcle

,2�

r.S

impl

ify

the

equ

atio

n a

nd

desc

ribe

wh

at i

t re

pres

ents

.

A�

�1 2�(�

r)(r

);A

��

r2;

the

area

of

a ci

rcle

Rea

din

g t

he

Less

on

4.T

he

form

ula

for

th

e ar

ea o

f a

circ

le u

ses

the

nu

mbe

r �

.How

doe

s th

isaf

fect

th

e va

lue

of t

he

area

of

a ci

rcle

fou

nd

usi

ng

the

form

ula

?S

amp

lean

swer

:Wh

en y

ou

su

bst

itu

te a

val

ue

for

�o

r u

se a

calc

ula

tor

to m

ult

iply

by

�,t

he

resu

lt w

ill b

e o

nly

an

esti

mat

e.

5.If

you

are

giv

en t

he

len

gth

of

the

diam

eter

of

a ci

rcle

,how

can

you

fin

d it

sar

ea?

Sam

ple

an

swer

:D

ivid

e th

e le

ng

th o

f th

e d

iam

eter

by

2,sq

uar

e it

,an

d m

ult

iply

th

e re

sult

by

pi.

Hel

pin

g Y

ou

Rem

emb

er6.

Th

ink

abou

t th

e fo

rmu

las

you

hav

e le

arn

ed t

hat

in

volv

e ci

rcle

s:C

�2�

ror

C�

�d

and

A�

�r2

.To

hel

p yo

u r

emem

ber

the

diff

eren

ce b

etw

een

th

efo

rmu

las

for

circ

um

fere

nce

an

d th

e fo

rmu

la f

or a

rea,

thin

k ab

out

the

diff

eren

ces

in t

he

un

its

use

d fo

r ea

ch m

easu

rem

ent.

Wh

at k

inds

of

un

its

are

use

d fo

r ea

ch?

How

can

th

is h

elp

you

rem

embe

r th

e fo

rmu

la f

or t

he

area

of

a ci

rcle

?S

amp

le a

nsw

er:T

he

un

its

for

the

circ

um

fere

nce

of

a ci

rcle

are

th

e sa

me

as t

he

un

its

for

the

dia

met

er o

r ra

diu

s o

f th

e ci

rcle

.Th

e u

nit

s fo

r th

e ar

ea o

f a

circ

le a

re a

lway

s sq

uar

e u

nit

s,so

th

at m

igh

t h

elp

yo

ure

mem

ber

th

at t

he

form

ula

fo

r th

e ar

ea o

f a

circ

le is

pi t

imes

the

squ

are

of

its

rad

ius.

Read

ing

to L

earn

Mat

hem

atic

sA

rea

of

Cir

cles

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Lesson 11–6



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mat

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App

licat

ions

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Con

cept

s, C

ours

e 2

Prac

tice:

Ski

llsA

rea

of

Co

mp

lex

Fig

ure

sF

ind

th

e ar

ea o

f ea

ch f

igu

re.R

oun

d t

o th

e n

eare

st t

enth

if

nec

essa

ry.

1.12

6.0

cm2

2.90

.3 m

m2

3.55

0 in

24.

59.1

in2

5.97

.8 m

26.

234

yd2

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m2

8.9.

1 ft

2

1.3

ft

1.3

ft

3.5

ft

3.5

ft

3.5

ft

3.5

ft4

m

4 m

2 m2

m

2 m

20 y

d

9 yd

11 y

d

9 yd

4 yd

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13 m

9 m

7 m

3 in

.4

in.

9 in

.15

in.

5 in

.

10 in

.

30 in

.

15 in

.

7 m

m5

mm

6 m

m

7 cm 7

cm

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Lesson 11–7

©G

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athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Stud

y Gu

ide

and

Inte

rven

tion

Are

a o

f C

om

ple

x F

igu

res

Fin

d t

he

area

of

the

figu

re a

t th

e ri

ght

in s

qu

are

feet

.

Th

e fi

gure

can

be

sepa

rate

d in

to a

rec

tan

gle

and

a tr

apez

oid.

Fin

d th

e ar

ea o

f ea

ch.

Are

a of

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tan

gle

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rea

of a

rec

tang

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8R

epla

ce �

with

12

and

ww

ith 8

.

A�

96M

ultip

ly.

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, b 1

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ultip

ly.

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e ar

ea o

f th

e fi

gure

is

96 �

32 o

r 12

8 sq

uar

e fe

et.

Fin

d t

he

area

of

each

fig

ure

.Rou

nd

to

the

nea

rest

ten

th i

f n

eces

sary

.

1.65

cm

22.

25.4

in2

3.80

6.1

mm

218

mm 38

mm

11 m

m

4 in

.5

in.

4 cm

6.5

cm

13 c

m

6 cm

6 cm

12 ft

4 ft

4 ft

12 ft

8 ft

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8 ft

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Co

mp

lex

fig

ure

sar

e m

ade

of c

ircle

s, r

ecta

ngle

s, s

quar

es,

and

othe

r tw

o-di

men

sion

al f

igur

es.T

o fin

dth

e ar

ea o

f a

com

plex

fig

ure,

sep

arat

e it

into

fig

ures

who

se a

reas

you

kno

w h

ow t

o fin

d, a

nd t

hen

add

the

area

s.



An

swer

s

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mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Read

ing

to L

earn

Mat

hem

atic

sA

rea

of

Co

mp

lex

Fig

ure

s

Pre-

Act

ivit

yR

ead

th

e in

tro

du

ctio

n a

t th

e to

p o

f p

age

498

in y

ou

r te

xtb

oo

k.W

rite

yo

ur

answ

ers

bel

ow

.

1.D

escr

ibe

the

shap

e of

th

e ki

tch

en.

rect

ang

le a

nd

sem

icir

cle

2.H

ow c

ould

you

det

erm

ine

the

area

of

the

kitc

hen

?S

amp

le a

nsw

er:

Fin

d t

he

area

of

the

rect

ang

le a

nd

th

e ar

ea o

f th

e se

mic

ircl

e,th

en a

dd

.

3.H

ow c

ould

you

det

erm

ine

the

tota

l sq

uar

e fo

otag

e of

a h

ouse

wit

h r

oom

s sh

aped

like

th

ese?

Sam

ple

an

swer

:F

ind

th

e ar

ea o

f ea

ch r

oo

m,t

hen

ad

d.

Rea

din

g t

he

Less

on

4.L

ook

up

the

term

foo

tage

in a

dic

tion

ary.

Wri

te t

he

mea

nin

g th

at m

atch

esth

e w

ay t

he

term

is

use

d in

th

is l

esso

n.

Sam

ple

an

swer

:le

ng

th o

r q

uan

tity

exp

ress

ed in

fee

t5.

Wh

at d

o yo

u t

hin

k th

e te

rm s

quar

e fo

otag

em

ean

s?S

amp

le a

nsw

er:

area

in s

qu

are

feet

6.W

hic

h w

ord

of t

he

com

pou

nd

squ

are

foot

age

indi

cate

s ar

ea?

Exp

lain

.S

amp

le a

nsw

er:

squ

are,

bec

ause

are

a is

mea

sure

d in

sq

uar

e u

nit

s7.

Loo

k u

p th

e te

rm t

wo-

dim

ensi

onal

in a

dic

tion

ary.

Sam

ple

an

swer

:h

avin

g t

wo

dim

ensi

on

s,es

pec

ially

len

gth

an

d w

idth

;p

lan

ar;

flat

8.N

ame

two

dim

ensi

ons

of e

ach

of

the

foll

owin

g fi

gure

s.

a.re

ctan

gle

b.

para

llel

ogra

mc.

tria

ngl

ele

ng

th a

nd

wid

thb

ase

and

hei

gh

tb

ase

and

hei

gh

t

9.R

efer

to

the

figu

re i

n E

xam

ple

2 on

pag

e 49

9.H

ow d

o yo

u k

now

th

at t

he

base

and

hei

ght

of t

he

tria

ngl

e ar

e ea

ch 4

in

ches

lon

g?S

amp

le a

nsw

er:T

he

len

gth

of

the

rect

ang

le is

10

inch

es,a

nd

th

e si

de

of

the

rect

ang

lew

her

e th

e tr

ian

gle

mee

ts t

he

rect

ang

le is

6 in

ches

lon

g p

lus

the

len

gth

of

the

sid

e o

f th

e tr

ian

gle

.So

,yo

u c

an s

ub

trac

t 6

fro

m 1

0 to

fin

d t

he

len

gth

of

the

sid

e o

f th

e tr

ian

gle

.

Hel

pin

g Y

ou

Rem

emb

er10

.L

ook

in a

dic

tion

ary

for

the

mea

nin

gs o

f th

e w

ord

com

plex

wh

en u

sed

as

an a

djec

tive

.Wri

te t

he

mea

nin

g of

th

e w

ord

as i

t is

use

d in

th

is l

esso

n.

Wh

y ca

n t

he

figu

res

in E

xam

ples

1 a

nd

2 be

con

side

red

com

plex

fig

ure

s?S

amp

lean

swer

:Th

e w

ord

co

mp

lex

mea

ns

“mad

e u

p o

f tw

o o

r m

ore

par

ts.”

Th

efi

gu

re in

Exa

mp

le 1

can

be

sep

arat

ed in

to a

rec

tan

gle

an

d a

sem

icir

cle;

the

fig

ure

in E

xam

ple

2 c

an b

e se

par

ated

into

a r

ecta

ng

le a

nd

a t

rian

gle

.

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

©G

lenc

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cGra

w-H

ill64

1M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Prac

tice:

Wor

d Pr

oble

ms

Are

a o

f C

om

ple

x F

igu

res

AR

CH

ITEC

TUR

EF

or E

xerc

ises

1–6

use

Jac

o’s

pre

lim

inar

y d

esig

n o

f h

is v

acat

ion

hou

se

at t

he

righ

t.R

oun

d t

o th

e n

eare

st t

enth

if

nec

essa

ry.

8 ft

4 ft 4 ft

4 ft

8 ft

4 ft

4 ft

4 ft

8 ft

8 ft

4 ft

4 ft

2 ft

4 ft

12 ft

4 ft

12 ft

16 ft

16 ft

12 ft

16 ft

16 ft4 ft

4 ft

bedr

oom

1ki

tche

nbe

droo

m2

b a t h r o o m

livin

gro

omde

n

NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

Lesson 11–7

1.W

hat

typ

e of

fig

ure

is

bedr

oom

1?

Fin

dth

e ar

ea o

f be

droo

m 1

.tr

apez

oid

;21

6 ft

2

2.W

hat

is

the

area

of

the

bedr

oom

2?

Wh

at f

igu

res

did

you

use

to

fin

d th

ear

ea?

224

ft2 ;

squ

are

and

rect

ang

le

3.W

hat

is

the

area

of

the

bath

room

?W

hat

are

th

e di

men

sion

s of

th

e fi

gure

syo

u u

sed

to f

ind

this

are

a?96

ft2

;8

ft b

y 4

ft r

ecta

ng

le a

nd

16

ft b

y4

ft r

ecta

ng

le

4.W

hat

is

the

area

of

the

livi

ng

room

?H

ow m

any

figu

res

did

you

use

to

fin

dth

is a

rea?

256

ft2 ;

Sam

ple

answ

er:

3

5.W

hat

is

the

area

of

the

den

? W

hat

wou

ld t

he

area

of

the

den

be

if t

he

sem

icir

cula

r w

indo

w w

ere

rem

oved

an

dre

plac

ed w

ith

a f

lat

win

dow

?19

8.3

ft2 ;

192

ft2

6.W

hat

is

the

area

of

the

kitc

hen

? If

Jac

oad

ds a

rec

tan

gula

r co

okin

g is

lan

d in

the

mid

dle

of t

he

kitc

hen

wit

hdi

men

sion

s 6

feet

by

4 fe

et,h

ow m

any

squ

are

feet

of

wal

kin

g sp

ace

wil

l be

left

?35

2 ft

2 ;32

8 ft

2



©G

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4M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Stud

y Gu

ide

and

Inte

rven

tion

Are

a M

od

els

and

Pro

bab

ility

A r

and

omly

-dro

pp

ed c

oun

ter

fall

s so

mew

her

e in

th

e sq

uar

es.F

ind

th

e p

rob

abil

ity

that

it

fall

s on

th

e sh

aded

sq

uar

es.

prob

abil

ity

�

�

Are

a of

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a of

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3.1

Sim

plify

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plify

.

So,

the

prob

abil

ity

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cou

nte

r fa

llin

g in

th

e sh

aded

squ

ares

is

abou

t �3 1. 51 �

orab

out

20.7

%.

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and

omly

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ed c

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ter

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s in

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e sq

uar

es.F

ind

th

ep

rob

abil

ity

that

it

fall

s in

th

e sh

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rite

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Rou

nd

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the

nea

rest

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th i

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eces

sary

.

1.10

%2.

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area

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area

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way

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lan

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sh

aded

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��

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�n

um

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of w

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to l

and

on s

quar

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NA

ME

____

____

____

____

____

____

____

____

____

____

DAT

E _

____

____

____

_P

ER

IOD

__

___

You

can

rela

te p

roba

bilit

y to

the

are

a of

geo

met

ric s

hape

s.

©G

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cGra

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3M

athe

mat

ics:

App

licat

ions

and

Con

cept

s, C

ours

e 2

Exte

nd

ing

th

e Py

thag

ore

an T

heo

rem

Th

e P

yth

agor

ean

Th

eore

m s

ays

that

th

e su

m o

f th

e ar

eas

of t

he

two

smal

ler

squ

ares

is

equ

al t

o th

e ar

ea o

f th

e la

rges

t sq

uar

e.S

how

th

at t

he

Pyt

hag

orea

n T

heo

rem

can

be

exte

nde

d to

in

clu

deot

her

sh

apes

on

th

e si

des

of a

tri

angl

e.T

o do

so,

fin

d th

e ar

eas

ofth

e tw

o sm

alle

r sh

apes

.Th

en,c

hec

k th

at t

hei

r su

m e

qual

s th

ear

ea o

f th

e la

rges

t sh

ape.

1.ar

ea o

f sm

alle

st s

hap

e:3.

5 in

22.

area

of

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bab

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1.

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Lesson 11–8

�1

23

45

6

11

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36


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13. C

I

B

F

C

G

D

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Chapter 11 Assessment Answer KeyForm 1 Form 2APage 649 Page 650 Page 651

(continued on the next page)


An

swer

s

14.

15.

16.

17.

18.

19.

20.

B:

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: �27

I

C

F

B

I

D

I

D

G

D

I

A

G

B

H

A

I

A

I

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�23

F

B

H

A

I

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Chapter 11 Assessment Answer KeyForm 2A (continued) Form 2BPage 652 Page 653 Page 654


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 14 in.

907.9 in2

113.1 cm2

288 mi2

476.7 m2

108 mm2

32 ft2

4.7 m

40 ft

8.5 cm

21.3

9.5

7

5

37

12

1,600

81

19

12 ft

30%

Chapter 11 Assessment Answer KeyForm 2CPage 655 Page 656


An

swer

s

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 12 ft

615.8 in2

38.5 ft2

576 cm2

57.1 in2

500 mm2

36 m2

7.8 cm

6.2 ft

75 m

17.9

8.9

9

6

33

11

900

16

83

14 mi

20%

Chapter 11 Assessment Answer KeyForm 2DPage 657 Page 658


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

B: 18.5 in.

1,170.2 m2

7,854.0 ft2

900 cm2

138.4 ft2

360 m2

160 cm2

10.0 in.

14.2 yd

48 m

30.5

8.2

12

9

16

21

1,024

361

259

24 ft

16.7%

Chapter 11 Assessment Answer KeyForm 3Page 659 Page 660


An

swer

s


Level Specific Criteria

4 The student demonstrates a thorough understanding of the mathematicsconcepts and/or procedures embodied in the task. The student hasresponded correctly to the task, used mathematically sound procedures,and provided clear and complete explanations and interpretations. Theresponse may contain minor flaws that do not detract from thedemonstration of a thorough understanding.

3 The student demonstrates an understanding of the mathematics conceptsand/or procedures embodied in the task. The student’s response to thetask is essentially correct with the mathematical procedures used and theexplanations and interpretations provided demonstrating an essential butless than thorough understanding. The response may contain minor errorsthat reflect inattentive execution of the mathematical procedures orindications of some misunderstanding of the underlying mathematicsconcepts and/or procedures.

2 The student has demonstrated only a partial understanding of themathematics concepts and/or procedures embodied in the task. Althoughthe student may have used the correct approach to obtaining a solution ormay have provided a correct solution, the student’s work lacks an essentialunderstanding of the underlying mathematical concepts. The responsecontains errors related to misunderstanding important aspects of the task,misuse of mathematical procedures, or faulty interpretations of results.

1 The student has demonstrated a very limited understanding of themathematics concepts and/or procedures embodied in the task. Thestudent’s response to the task is incomplete and exhibits many flaws.Although the student has addressed some of the conditions of the task, thestudent reached an inadequate conclusion and/or provided reasoning thatwas faulty or incomplete. The response exhibits many errors or may beincomplete.

0 The student has provided a completely incorrect solution oruninterpretable response, or no response at all.

Chapter 11 Assessment Answer KeyPage 661, Extended Response Assessment

Scoring Rubric

An

swer

s


Chapter 11 Assessment Answer Key Page 661, Extended Response Assessment

Answer Key

1. a. The square root of a number is one ofits two equal factors.

b.

�17� � 4

c. In a right triangle, the square of thelength of the hypotenuse is equal tothe sum of the squares of the lengthsof the legs.

d.

e. No, �482 �� 362� equals 60, not 62.

f. Use the Pythagorean Theorem.

a2 � b2 � c2

302 � 362 � c2

900 � 1,296 � c2 Find the squares.

2,196 � c2 Add.

�2,196� � c Find the square root.

46.9 � c

2. Find the area of the trapezoidal parkand subtract the areas of the circularfountain and triangular botanicalgarden. Multiply this area by the costper square foot.

Area � �12� � 175(300 � 350) � �202

� �12� � 145 � 125 � 46,556

Mrs. Cobel’s bid:46,556 � $1.50 � $69,834

4

4

4 � 4 17�

�

In addition to the scoring rubric found on page A28, the following sample answersmay be used as guidance in evaluating extended response assessment items.

1. false; square

2. true

3. false; hypotenuse

4. false; angle

5. false; hypotenuse

6. true

7. false; radical

8. true

9. false; complexfigures

10. true

11. a theorem that saysthat in a righttriangle, the squareof the length of thehypotenuse equalsthe sum of thesquares of thelengths of the legs

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

Quiz (Lessons 11-3 and 11-4)

Page 663

1.

2.

3.

4.

5.

1.

2.

3.

4.

5.

Quiz (Lessons 11-7 and 11-8)

Page 664

1.

2.

3.

4.

5. 13.3%

20%

30%

25 in2

76.8 ft2

10.2 cm2

50.3 in2

792 ft2

1,950 mm2

3,840 m2

663 ft2

38.3 m2

21 mm

7.9 cm

50 ft

1715

12826196

1,2961,849529

Chapter 11 Assessment Answer KeyVocabulary Test/Review Quiz (Lessons 11-1 and 11-2) Quiz (Lessons 11-5 and 11-6)

Page 662 Page 663 Page 664


1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13. 7.1 in2

31.5 mm2

5.24 m

11

y

xO

R'

P'

PQ'

Q

R

P�(�2, 0); Q�(0, 3);R�(3, �2);

No; 144° does notdivide evenly into 360°.

the chance of nosnow; 55%

250%

�56090

�

4

29�14

�

�12

�

�18e

3.6 m

20.2 m5 cm

2017

1815

25681

H

B

F

D

F

C

Chapter 11 Assessment Answer KeyMid-Chapter Test Cumulative ReviewPage 665 Page 666


An

swer

s

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13. 14.

15.

16.

17. a.

b. 17.0 ft

pole21 ft

board27 ft

x ft

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

01 0

120 outcomes

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

63

0 0 0 0 01 1 1 1 12 2 2 2 23 3 3 3 34 4 4 4 45 5 5 5 56 6 6 6 67 7 7 7 78 8 8 8 89 9 9 9 9

55 .1

�14, �10, �8,�3, 0, 11

DCBA

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

IHGF

DCBA

Chapter 11 Assessment Answer KeyStandardized Test PracticePage 667 Page 668


CH 11

Documents

introduced

rectangular

famous baseball

proposed building

single world

fertilizer

dropped counter

compound square