Lesson 26 MGSE4.MD.3 Perimeter and Areakarladavis.weebly.com/uploads/3/7/4/5/37452469/...Perimeter and Area a. To solve the problem, do you use perimeter or area? Explain how you know.

Introduction

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Use What You Know

Lesson 26 Perimeter and Area

Lesson 26Perimeter and Area

a. To solve the problem, do you use perimeter or area? Explain how you know.

b. How do you find the perimeter of a rectangle?

c. How much fencing is there in all?

d. What is the length of the garden? How many sides of this length does the

garden have? What is the total length of these sides?

e. How much fencing is left to make the other two sides? Explain how to find

this length.

f. Explain how you can find the length of the other two sides of the rectangle.

Marissa has 64 feet of fencing. She is using the fencing to border a rectangular flower garden. Marissa wants the length of the garden to be 20 feet. If she uses all of the fencing, what will be the width of the rectangular garden?

You have learned that you can find the perimeter of a rectangle by adding the lengths of the sides. Take a look at this problem.

20 feet? feet

MGSE4.MD.3

MGSE4.MD.8

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Find Out More

Rectangles have length and width.

width width

length

length

To find the perimeter of a rectangle, you can add the sides in any order.

Perimeter 5 length 1 length 1 width 1 width

Since the opposite sides of a rectangle are the same length, you can rewrite the equation as:

Perimeter 5 2 3 length 1 2 3 width

Use P to stand for perimeter, < to stand for length, and w to stand for width:

P 5 2 3 < 1 2 3 w or P 5 2< 1 2w

The equation above is called the perimeter formula. Here is how to solve the problem from the previous page using the formula.

64 5 (2 3 20) 1 (2 3 w) 64 5 40 1 (2 3 w)

Now subtract: 64 2 40 5 24.

With 24 feet of fencing left, the width of the rectangle must be 24 4 2, or 12 feet.

Later in the lesson, you will solve problems about area.

Reflect1 The perimeter of a rectangular poster is 14 feet and the length is 4 feet. Describe

how to use the perimeter formula to find the width.

Modeled and Guided Instruction

Learn About


Lesson 26


Solving Perimeter Problems

Read the problem below. Then explore different ways to solve perimeter problems.

Keegan is building a rectangular play area in his backyard for his dog. The length of the rectangle is 30 feet and the width is 24 feet. What amount of fence does Keegan need to buy to make the play area?

Picture It You can use models to help solve perimeter problems.

Draw a picture to represent the fence.

You can use color to highlight the sides that have the same length.

30 ft

24 ft

Add the lengths to find the amount of fence Keegan needs to buy.

30 feet 1 24 feet 1 30 feet 1 24 feet

Model It You can also use words to help solve perimeter problems.

In this rectangle, the length is 30 feet and the width is 24 feet.

There are two sides that have a length of 30 feet and two sides that have a length of 24 feet.

amount of fence 5 length 1 length 1 width 1 width 5 30 feet 1 30 feet 1 24 feet 1 24 feet


Connect It Now you will solve the problem from the previous page using a formula.

2 What formula can you use to find the amount of fence Keegan needs? Why?

3 Use the formula to find the amount of fence Keegan needs for the dog’s play area.

4 Keegan uses the formula P 5 2(< 1 w) to find the amount of fence he needs. Does Keegan’s formula work? Why or why not?

5 Which formula do you think is easiest? Why?

6 Explain when to use the formula for the perimeter of a rectangle.

Try It Use what you just learned to solve these problems. Show your work on a separate sheet of paper.

7 Bianca is fencing in a garden. She wants the garden to be a rectangle 15 feet by

10 feet. How much fence does she need to buy to make her garden?

8 Michael glues pipe cleaners around the edges of a rectangular poster. He uses a total of 14 pipe cleaners with 5 pipe cleaners each on the longer sides of the poster. How many pipe cleaners does he use for each of the shorter sides of

the poster?


Learn About


Lesson 26


Solving Area Problems

Read the problem below. Then explore different ways to solve area problems.

Kevin is making a rectangular mural using colored tiles. He buys enough tiles to cover an area of 112 square feet. Kevin wants the width of the mural to be 8 feet. If he uses all of the tiles, what is the length of the mural?

Picture It You can use a picture to help solve area problems.

Make a sketch of the mural.

? feet

8 feet 112 square feet

Since you multiply the length and width of a rectangle to find the area, think: 8 3 ? 5 112.

Model It You can use words to help understand the problem.

area of the mural 5 length 3 width

The area of the mural is 112 square feet.

It can be covered by 8 rows of units that are each 1 square foot.

The number of square-foot units in each row is the length of the mural.


Connect It Now you will solve the problem on the previous page using a formula.

9 Write an equation to represent the area of the mural.

10 Describe how you can find the length of the mural.

11 If Kevin uses all the tiles, what is the length of the mural?

12 Kevin notices another package of tiles that makes a mural with an area of 152 square feet. Write an equation that can help you find the length of this mural

if it is also 8 feet wide.

13 Find the length of the mural Kevin can make with the package of tiles that covers

an area of 152 square feet.

14 Suppose that you know the length and area of a rectangle. How would you find

the width?

Try It Use what you just learned to solve these problems. Show your work on a separate sheet of paper.

15 Carla wants to create a garden in her backyard. She wants the width of the garden to be 9 meters and the area to be 162 square meters. What length should she

make the garden?

16 Bill is building a deck. He wants the length of the deck to be 7 feet. If he wants the area of the deck to be 105 square feet, what will be the width of

the deck?


Learn About


Lesson 26


Read the problem below. Then explore using rectangles to find the area of a shape.

Harry sews this patch on the back of his jacket. What is the area of the patch?

Picture It You can draw the figure on a grid and count the grid squares.

2 in.

10 in.

4 in.

4 in.

3 in.

2 in.

Model It You can break the figure apart into rectangles and find the area of each rectangle.

2 in.

2 in.10 in. 10 in.

3 in.

2 in.

Solving Problems by Adding Areas

2 in.

10 in.

4 in.

4 in.

3 in.

2 in.


Connect It Now you will solve the problem on the previous page by adding areas.

17 Find the area of the patch by counting the squares in Picture It.

18 Use the formula for the area of a rectangle to find the area of each rectangle in

Model It.

19 Add the areas to find the area of the patch and compare the result with your

answer to problem 17.

20 Now break the patch into five rectangles. Find the area of the patch using these rectangles.

21 Is the area of the patch the same when you break it into five rectangles as when

you break it into three rectangles? Explain.

Try It Use what you just learned about adding areas to solve these problems.

22 A swimming pool is the shape below. What is the area of this figure?

6 m

12 m

4 m8 m

23 Students plant a vegetable garden in this shape. What is the area of the garden?

12 ft

2 ft

3 ft

4 ft

2 in.

10 in.

4 in.

4 in.

3 in.

2 in.

Guided Practice

Practice


Lesson 26


Solving Perimeter and Area Problems

Example

Pair/ShareHow else could you solve the problem?

Pair/ShareHow did you solve the problem? Why did you choose that method?

Are you looking for the perimeter or the area of the pool?

The student uses a formula for perimeter of a rectangle and labels the work to keep it organized.

24 A designer is adding a border around the edge of a rectangular swimming pool. He measures the pool and finds that the length of the pool is 52 meters and the width is 26 meters. How long is the tile border?

Show your work.

Solution

Jen drew a rectangle with a length of 12 inches and a width of 10 inches. Then she drew another rectangle by doubling the length and width of the first one. What is the perimeter of the second rectangle?

Look at how you could show your work using a formula for perimeter.

P 5 2(< 1 w)

length and width of first rectangle: < 5 12 inches and w 5 10 inches

length and width of second rectangle: < 5 12 3 2, or 24 inches, and w 5 10 3 2, or 20 inches.

Perimeter of second rectangle 5 2(24 1 20) P 5 2 3 44 P 5 88

Solution

Study the example below. Then solve problems 24–26.

The perimeter of the second rectangle is 88 inches.


Pair/ShareDoes Tricia’s answer make sense?

Pair/ShareHow do the units in the answer tell whether you found area or perimeter?

Are you finding the perimeter or the area of the room?

How much area can Tricia cover with all the bags of pebbles?

25 Zachary is getting new carpet in his bedroom. The dimensions of his room are shown in the diagram below. How much carpet does he need to cover the whole floor?

8 ft

8 ft6 ft

5 ft

Show your work.

Solution

26 Tricia wants to create a path using pebbles. She has 8 bags of pebbles and each bag covers an area of about 6 square feet. If she wants to make the path 2 feet wide, about how long can she make the path? Circle the letter of the correct answer.

A 3 feet

B 22 feet

C 24 feet

D 48 feet

Tricia chose A as the correct answer. How did she get that answer?

Independent Practice

Practice

©Curriculum Associates, LLC Copying is not permitted.284 Lesson 26 Perimeter and Area

Lesson 26

Solving Perimeter and Area Problems

Solve the problems.

1 There is a new playgound at the park. What is the area of the playground shown in the diagram below?

A 20 square meters

B 40 square meters

C 42 square meters

D 49 square meters

2 The diagram shows the garden Mike has next to his garage. He wants to put a fence around the three sides of the garden that do not border the garage. Which expression does NOT represent the amount of fence Mike needs to buy?

A 6 1 21 1 6

B 2w 1 ø

C 2w 1 2ø

D 2 3 6 1 21

3 Maya is finding the perimeter of the rectangle at the right. Which expression(s) can be used to find the perimeter? Circle the letter for all that apply.

A (2 3 16) 1 (2 3 12)

B 2 3 16 1 12

C 2(16 1 12)

D 16 3 12

E 16 1 12 1 16 1 12

Garden

Garage

21 feet

6 feet

12 in.

16 in.

7 m

4 m

3 m

3 m2 m

1 m

Self Check


4 A rectangle is 22 feet long and has a perimeter of 56 feet. What is the width

of this rectangle?

5 Ms. Leone decides to make a raised garden bed for her backyard. Her plan for the garden bed includes the following:

• It will be in the shape of a rectangle.

• The sides of the bed will use a total of 30 feet of cedar boards.

• Each side will be longer than 1 foot.

• The length and width will measure whole feet.

Part A Use the grid below to draw three different rectangles that can each represent Ms. Leone’s garden bed. Be sure to use all 30 feet of the boards for each bed.

5 1 square footKey

Part B Write the length and width of each garden bed you drew. Then find the area of each garden bed.

Garden Bed 1: Garden Bed 2: Garden Bed 3:

Length: Length: Length:

Width: Width: Width:

Area: Area: Area:

Go back and see what you can check off on the Self Check on page 239.

Lesson 26 MGSE4.MD.3 Perimeter and Areakarladavis.weebly.com/uploads/3/7/4/5/37452469/...Perimeter and Area a. To solve the problem, do you use perimeter or area? Explain how you know.

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