Name

Measure Perimeter

The distance around a dosed figure is called the

Math in My WorldExample 1Berto walked around a park on the rectangularpath shown- How fat did Berto walk?

Opposite sides of a rectangle are equal. So, the side

lengths are 12 yards, 12 yards, 6 yards, and 6 Y&ds.

Add the measures of au of the sides of the figure.

Perimeter 12 yards + 12 yards + 6 yards + 6 yat&

Perimeter =

So, Berto walked

Key Concept

yards

yards.

i

Lesson I

ESSENTIAL QUESTIONWhy is to

areal

12 yd

825

.1

Words To God the penmeter 01 a rectangle. odd the lengthsof the The perimeter of a rectangle also equals2 bmes 'ts length plus 2 times its widttv

Content at

A square has four sides of equal length. ro find the perimeterof a square, multip&y the length of one side by four.

Example 2Find the perimeter of a square with

side lengths Of 6 inches.

One Way Add fre measures of all of thesides of the figure.

P 6 inches + 6 inches 6 inches 4 6 inches

P 24 inches

Another Way use a formula

Multip&y the length of one side by 4 because there

are 4 sides of equal length.

s ts equS to one Side length

6 in.

6 in.

6 in.

p x 6 inches

p 24 inches

So, the perimeter of the square is

Guided Practice

Find each perimeter.

g cm

2.

826

inches.

Descrbe two

ways to find the

perimeter of a

square.

Nome

Independent Practice

Find each perimeter.

8 mm

6 mm

8 mm

15 cm

12ft

12ft

12tt

Algebra Find the unknown side Length. Write an equation to find

the perimeter.

10Yd

The unknown side length is

Find the perimeter of each rectangle in units.

4 in.

4 in. ? in.

4 in.

The unknown side length is

Lesson I Meuse Perimeter 827

t) Problem SolvingUse the picture of a footban field for Exercises 11—12.

Wt',at is the petimetet of the foocball field without

the end zones?

12. Each end zone is 10 yards long What is theperimeter of the entire football field in feet?

PRACTICE Use Number Sense A baseballdiamond is shaped Lke a square. The perimeter is

360 lect. What is the length of each side?

14. PRACTICE Explain to a Friend Explain to a

friend how to find the perimeter of the figure Shownto the right

15. Building on the Essential Question How can a formula helpme to find perimeter?

828 Chapter 13 Penmeter and

160

10 ft

Name

Hands OnModel Area

A square with a side length of one unit is calleda unit square.

A unit square has one square unit of area and can beused to measure area Area is the number of square

units needed to CO•eet a figure without overlapping,

Draw It

Find the area of the rectangles shown in the table.

Rectangle I - Length

(units)

Draw each rectangle.

Width

(units) (sq units)

Use grid paper to draw each rectangle.

Find the length and width of each rectangle.Count the number of unit squares frat coyer the length

and width of the rectangle- Record each in the table.

Determine the area Of each rectangle.

Count the number of whole squares that cover

the rectangle. Each whole square is I square unit.

Colire Contert at

Dola

Lesson 3

ESSENTIAL QUESTIONis it important to

measÜe perimeterand area?

Sha&ng. oc covering.o unrt qlt.jore

tn one squate t»ntt

Lessen 3 839

Try It

Find a formula that can be used to find the

area of a rectangle.

Measure the length and width of eachobject listed in the table.

Use a centimeter ruler to measure the

length and the w•dth of eoch object to the

nearest centimeter. Record the results in the table.

Crayons24

length

width

Area

(sq an)

Find the area of each object-

Use what you learned in the first

example to estimate the area of each

Draw rectangles on grid paper.Then count the unit squares to find

the area. Record the results.

Justify the formula for area.

took for a pattem to find how lengthand width relate to area,

I LengthObject

(cm)

sticky mte

box

book

Width

The area of each object is the product of the

and

Talk About It

t. How did you make yout estimates for the orcas of the objectsin Activity 2? How dose were the estimates to the actual areas?

2. Wl•.at operation can you use with the length and the width

to equal the area of a rectangle? Explarn,

S• PRACTICE Use Symbols What s the formula for the area Of arectangle? Use A for area. for length. and w for 'Mdth.

840 Chapter Penn-eter ond

Nerrve

Practice It

Complete the table below.

Rectangle

agnnaa

I Length (units)

o

Width (units)

D

I Area (sq units)

Lesson 3 Cn: Area 841

Apply It

Use the area formula you wrote in Exercise 3

to solve each problem.

9. ML Hart is hangng a pidure on a wall. The pictureframe has a length of 12 inches and a Width of

9 oches. How much wail space wili the picture need?

'O. What is the area of a dassroom with a length

04 30 feet and a width of t S feet?

Miss Foster wants to buy carpet for her living room.

the living room has a length of IS feet and a width

of 10 feet Hcy.v much carpet "ill she need?

12• PRACTICE Use Math Tools Rickfs monitor

is a rectangle. The length is 15 inches and the width is 12 inches.

Estimate the area of the monitor.

Write About It

IS. Suppose two rectangles have the same area. Wast they have the

same length and width? Explain.

842 Area

i

Nome

Measure Area

You know that area is the number of sqnre units

needed to cover a region Of figure without any

Math in My WorldExample 1the Perez family wants to put the sandbox

shown in their backyard. mat is the area ofthe sandbox?

One Way Count unit squares.

Tile the rectangle with unn squares. Each '.nit

square has an area of one separe foot.

toft

Dala

Lesson 4

ESSENTIAL Q*STtON

measure

and area?

Another Way Multiply.

Muttiply the length times the width to

find the area.

A length x width

A = 10 feet x S feet

square feet

There are

There are

unit squares.

square feet

So, the area of the sandbox is square feet

i

Key Concept Area ofa Rectangle

To the A Of a rectangle, mulEp(Y the letgth Cby the Width w.

SymbolsW w

Find the measure of the missing side

A = S x S Wute tt•e gormuta.

64 8 x S

Think: 8 times what number equals 64?

meters

The measure of the missing side is

Guided Practice

Find the area of each square or rectangle.

You can also find the area of a square.

Key Concept

1.

Words

Symbols

To find the area A of a square, mult4)ty the lengthot one 9de s by Self.

s

s

s

Example 2The area •nd the measure of one side of the square is given.

meters.

Area 64 sq m

Describe two

ways to find the

area of a sepate.

2. S yd

846 Chapte Pnmeter "d Area

Name

Independent Practice

Find the area Of each square or rectangle.

nan—nana

10 yd

Algebra The area and the measure of one side of each square

ot rectangle are given. Label the missing sides.

847

7 in.

Area — 49 square inches

Area = 5 square centimeters

Area — 32 square meters

6 in.

Area — 24 square inches

Lesson4 Measure Area

t) Problem SolvingEach child in Dixon's class has a

rectangular ru»tebook that has an area

of 108 square inches. If the notebook

is 9 inches w€de, what is the length ofthe

12. A cat is 15 feet long md 6 feet wide, It is parkedon o rectangular driveway with an areo of I t 2 square

feet. How much of the driæ.vay is not coveted bythe car?

IS. PRACTICE Plan Your Solution A rectangularpldtground is 40 meters by 10 meters. Its area will

be cm•ered with shredded tires. Each bag of shredded

tires covers 2(X) quare meters and costs $30 findthe cost for this project

14• PRACTICE Reason A square has sides measuring 3 feet If thesides of a square are doubled, will the area also double? Explain.

IS. Building on the Essential Question How can estimation helpme to find the area of a rectangle ot square?

848 Chapte Penmetet Area