10.1 Areas of Quadrilaterals and triangles · PDF file10.1 Areas of Quadrilaterals and triangles ... find the length of its median. ... An isosceles trapezoid with legs of 6 m. and

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10.1 Areas of Quadrilaterals and triangles

BASE AND HEIGHT MUST FORM A RIGHT ANGLE!! Draw the diagram, write the formula and SHOW YOUR WORK!

FIND THE AREA OF THE FOLLOWING: 2. A rectangle with one side of length 12 mm and

1. A square with diagonal of length 12 m. The perimeter 40 mm.

3. A parallelogram with base 7 m and height 3 m. 4. A rectangle with diagonal of length 17 cm and base

length of 15 cm.

5. An isosceles with base length 10 cm and 6. An equilateral with perimeter of 27 cm.

36 perimeter cm.

7. A parallelogram with sides 8 cm and 10 cm and an 8. A trapezoid with bases 13m and 21 m and height 5m.

angle of 60.

9. A triangle with sides of lengths 8, 15, 17. 10.

11.

18

15

6

9

15

7

2

12. All consecutive sides are perpendicular.

13.

Find each missing measure.

14. The area of a triangle is 216 square units. If the height is 18 units, what is the length of the base?

15. The area of a trapezoid is 80 square units. If its height is 8 units, find the length of its median.

(median = average of the bases)

16. The height of a trapezoid is 9 cm. The bases are 8 cm and 12 cm long. Find the area.

17. A trapezoid has an area of 908.5 cm2. If the altitude measure 23 cm and one base measures 36 cm, find the length of the other

base.

18. The measure of the consecutive sides of an isosceles trapezoid are in the ratio 8:5:2:5. The perimeter of the trapezoid is 140

inches. If its height is 28 inches, find the area of the trapezoid.

19. A kite has diagonals of 5ft. and 11.3 ft. What is the area of the kite?

3. Find the area of a rhombus whose perimeter is 20 cm and whose diagonal is 8cm. ________

4. Find the area of a square with a diagonal of length 3.

5

7 6

2

5

2

5

6

60˚ 60˚

6 6

10

3

10.2 Circle and Regular Polygons

7. Regular hexagon with side 8 cm.

Regular Polygons:

Apothem = ____________________________________________________ Area = ________

a = _______

s = _______

p = _________

A = ___________

a = _______

s = _______

p = _________

A = ___________

a = _______

s = _______

p = _________

A = ___________

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Find the AREA of the figure. Draw diagram if needed. Show formula that you are using!

1. Square with a diagonal of 14 m. 2. Rectangle with length of 24 in. and diagonal of 25 in.

3. Parallelogram with sides 10 and 16 and a 30 angle. 4. An equilateral triangle with side of 15 yd.

5. Regular Hexagon with apothem of 3 cm. 6. Rhombus with diagonals of 14 and 12 meters.

7. An isosceles trapezoid with legs of 6 m. and bases of 10 m and 8 m. 8. Circle with circumference of 16.

10.3 Composite Figures

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10.3 Composite Figures

Find the shaded area. Round to the nearest tenth if necessary.

1.

2.

3.

4.

5.

6.

7.

8.

6

10.5

SCALE FACTOR = Ratio of 2 corresponding sides in 2 similar polygons

Scale Factor= ratio of 2 heights/ ratio of 2 radii/ ratio of 2 bases/ ratio of 2 diameters …

Are all triangles similar?________Are all squares similar?______ All rectangles? _____ All circles? _________

Scale Factor: b

a

Ratio of Perimeters: b

a

Ratio of Areas: 2

2

b

a

Ratio of Volume: 𝑎3

𝑏3

Ex. 1 The ratio of the perimeters of 2 similar triangles is 3: 4.

Find the ratio of their areas. _____________

Ex. 2 The ratio of the areas of 2 circles is 16 : 49.

Find the ratio of their diameters. ______________

Ex. 3 The perimeters of 2 similar quadrilaterals are 48 and 60. The area of the smaller quadrilateral is 96 cm2. Find the

area of the larger quadrilateral.

Ex. 4 The areas of 2 similar triangles are 36 and 64. The length of a side of the smaller triangle is 12. Find the length of

the corresponding side of the larger triangle.

Describe the effect of each change on the area of the given figure.

1. The base of the parallelogram is multiplied by 3

4.

2. The length of a rectangle with length 12 yd and width 11 yd is divided by 6.

3. The base of a triangle with vertices A(2, 3), B(5, 2),

and C(5, 4) is doubled.

4. The height of a trapezoid with base lengths 4 mm

and 7 mm and height 9 mm is multiplied by 1

3.

In Exercises 5–8, describe the effect of each change on the

perimeter or circumference and the area of the given figure.

5. The length and width of the rectangle are multiplied by 4

3.

6. The base and height of a triangle with base 1.5 m and height 6 m are both tripled.

7

7. The radius of a circle with center (2, 2) that

passes through (0, 2) is divided by 2.

8. The bases and the height of a trapezoid with base lengths

4 in. and 8 in. and height 8 in. are all multiplied by 1

8.

9. A rhombus has an area of 9 cm2. The area is multiplied by 5.

Describe the effects on the diagonals of the rhombus.

10. A circle has a circumference of 14 ft. The area is halved.

Describe the effects on the circumference of the circle. Find the similarity ratio for each pair of similar figures.

11. Two regular hexagons with areas 8 in.2 and 32 in.2 12. Two squares with areas 81 cm2 and 25 cm2

13. Two ∆’s with areas 10 ft2 and 360 ft2 14. Two circles with areas 128π cm2 and 18 π cm2.

For each pair of similar figures, the area of the smaller figure is given. Find the area of the larger figure.

15. 16. 19.

For each pair of similar figures, find the ratio of the perimeters.

17. 18. 22.

19. The shorter sides of a rectangle are 6 ft. The shorter sides of a similar rectangle are 9 ft. The area of the smaller rectangle is 48

ft2. What is the area of the larger rectangle?

12 in 5 in

A = 20 in 2

7 cm

A = 84 cm 2

15 cm

5 in 7 in A = 18in2

8 in

A = 12 cm 2

A = 27 cm 2

A = 1 in 2

A = 4 in 2 A = 50 cm 2

A = 8 cm 2

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10.6 Probability is the chance or likelihood that an event will occur.

Probability = 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑜𝑢𝑡𝑐𝑜𝑚𝑒

𝑡𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠

Ex. 1 There are 30 students in this class and 18 are male. If you choose a student from the class, what is the probability

that you will pick a female student. (answer as a % )

Probability with lengths: 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑙𝑒𝑛𝑔𝑡ℎ

𝑡𝑜𝑡𝑎𝑙 𝑙𝑒𝑛𝑔𝑡ℎ

Ex. 2 A point X is picked at random on 𝐴𝐹̅̅ ̅̅ . What is the probability that X is on:

a) 𝐴𝐶̅̅ ̅̅ b) 𝐶𝐸̅̅̅̅ c) 𝐴𝐹̅̅ ̅̅

10.6 Probability with Areas: 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑎𝑟𝑒𝑎

𝑡𝑜𝑡𝑎𝑙 𝑎𝑟𝑒𝑎

Use the square dart board for the following:

The radius of the bull’s eye is 4 cm.

The radius of the middle circle is 8 cm.

The radius of the largest circle is 12 cm.

ROUND PERCENTS TO NEAREST TENTHS

Ex. 3) Suppose you throw a dart onto the square dartboard ,

find the probability that the dart will land:

a) in the bull’s eye b) in the shaded area:

A B C D E F

-5 -1 4 10 16 20 40 cm

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Ex 4. Find the probability that if a point is chosen inside the square, Ex. 5 Find the probability that if a point is

it will lie outside the circle. inside the hexagon, it will lie in the

shaded region.

Ex. 6 Find the probability that if a tack is dropped in the rectangle, it will land

a) in the circle

b) outside of the circle

Ex. 7 To win a carnival game, Max must throw a dart at a board four feet by three

feet and hit one of the 25 circles on the board. The diameter of each circle is 4

inches. Approximately what percent of the time will a randomly thrown dart that

hits the board also hit a circle?

Ex. 8 A rectangle contains two inscribed semicircles and a full circle, as shown

below. If a point is chosen at random inside the rectangle, what is the approximate probability that the point will also be

in the shaded region?

Thee dart board shown has 5 concentric circles whose centers are also the center of the square board. Each side of the board is 38

cm, and the radii of the circles are 2 cm, 5 cm, 8 cm, 11 cm, and 14 cm. A dart hitting within one of the circular regions scores the

number of points indicated on the board, while a hit anywhere else scores 0 points. If a dart, thrown at random, hits the board, find

the probability of scoring the indicated number of points.

7. 0 points 8. 1 point 9. 2 points

10. 3 points 11. 4 points 12. 5 points

Find the probability that a point chosen at random from

AK is on the given segment.

4. CF 5. BI 6. GK 7. FG 8. AK 9. AC

5

4

3

2

1 0

0

A B C D E F G H I J K

16 14 2

4 6 8 10 12 18 20

11 in.

6

10

11. That state of Connecticut is approximated by a rectangle 100 mi by 50 mi. Hartford is approximately at the center of the state.

If a meteor hit earth within 200 mi of Hartford, find the probability that the meteor landed in Connecticut.

12. A stop light at an intersection stays red for 60 second, changes to green for 45 seconds, and then yellow for 15 seconds. If Joel

arrives at the intersection at a random time, what is the probability that he will have to wait at a red light for more than 15 seconds?

Find the area of the following:

1. 2.

3. All consecutive sides are

4.

7. 8. 9.

Area= ________ scale factor:_________

Circum.=______ ratio of perimeters:________ Area: _________

Ratio of areas: _________

10. Find the base of a rectangle with height 7 cm and area 91 cm2.

12. Find the area of a rhombus whose diagonals are 8 cm and 12 cm long.

13. Find the height of a trapezoid with longer base 30 cm, shorter base 12 cm, and area 105 cm2.

14. Find the area of a regular hexagon whose radius is 24 in.

15. Find the area of an equilateral ∆ whose side is 8 mm.

16. If 2 octagons are similar with a scale factor of 4:7, find the ratio of their areas.

17. Isosceles trapezoid ABCD has bases AB = 37 and CD = 13. If XD = 17, the area of XYCD is what % of the area of ABCD?

18. The area of parallelogram with bases of 6 cm and 12cm and one angle of 30 is ___?

19. The area of a circle is 75 . Find the Circumference in terms of .

1. A 30-60-90 triangle has a hypotenuse of length 32 cm. What is the area of the triangle?

13 5 12

8

3

3 2

7 2

4

6

30

312

2.5

20 20

32

6

15

B C

A D

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2. An isosceles right triangle has a hypotenuse with length 10 . What is the area of the right triangle?

3. In the diagram, rhombus ABCD has area 216 m2 and BD = 18m. Find CA.

4. In the diagram, the perimeter of EFGH is 50 mm. If EF = 12 mm, what is the area of the rectangle?

5. A 45-45-90 triangle has an area of 50 units2. What is the length of the hypotenuse?

6. What is the area of a parallelogram with a 45 degree angle and sides of length 6 cm and 7 cm?

7. In the diagram, parallelogram TRAC has TR = 12, RA = 14, and RK = 10. What is the area of the parallelogram?

8. A trapezoid has an area of 33 cm2. Find the longer base if the shorter base is 4cm and the height is 6 cm.

9. In the diagram, ABCDE is a regular pentagon with side lengths 6m. OX = 4.13 m .

Find the area to the nearest tenth of a meter.

10. What is the area of a regular triangle with a radius of 8 units?

13. A regular hexagon has a side of length 8 cm. Find the area of the hexagon.

14. Two regular pentagons have sides of 14m and 3.5 m, respectively. Find their scale

factor, ratio of their perimeters and areas.

15. Two regular octagons have perimeters 16 cm and 32cm, respectively. Find the scale

factor and the ratio of their areas.

16. Two similar polygons have a scale factor 7 : 5. The area of the larger polygon is 147 u2.

Find the area of the smaller polygon.

17. The areas of 2 circles are 100 and 36. Find the ratio of their radii and their circumferences.

18. The circumference of a circle is 26. Find its area.

F E

H G

A R

T K C X D E

O A

B

C

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Chapter 10 – Area of 2D Shapes

Area of a square: s2 Perimeter of a square: 4s

Area of a Rectangle: bh Perimeter of a Rectangle: 2b + 2h or (2l + 2w)

Area of a Triangle: 2

bh or bh

2

1 Equilateral : 4

32s

Area of a Parallelogram: bh

Area of a Rhombus or Kite: 2

21 dd or 212

1dd

Area of a Trapezoid:

221 hbb

or 212

1bbh

Area of a Circle: r2 Circumference of a Circle: 2r or d

2

360: r

arcofmeasureSectoraofArea

Tuesday

4/5

10.1 and 10.2 Areas of Triangles and

Quadrilaterals, Circles, and Regular

Polygons

Packet Pages 1-4

HW:

HW and Packet Pages 1-4 are due on Wednesday 4/13

Thursday

4/7

Keys Trip

10.1 and 10.2 Review

Packet Pages 1-4

Yackey not in class

HW and Packet Pages 1-4 are due on Wednesday 4/13

Monday

4/11

Keys Trip

More Review

Yackey not in class

HW and Packet Pages 1-4 are due on Wednesday 4/13

Wednesday

4/13

10.3 Composite Figures

Review 10.1-10.3

Packet Pages 5

HW:

Friday

4/15

QUIZ #1 10.1-10.3

10.5 Ratios of Similar Figures

Packet Pages 6-8

HW:

Tuesday

4/19

10.6 Geometric Probability

Packet Pages 8-10

HW:

Thursday

4/21

QUIZ #2

Review

Packet Pages 10-11

HW: Finish Packet

Monday

4/25

Unit 10 Test

TURN IN PACKET AT BEGINNING OF CLASS

HW: None :)