7th Grade Math

Get ConnectED

Similarity and Proportional Reasoning

PART A B CDE

Multi-Part

Lesson 3

GLE 0706.4.3

Understand and use scale

factor to describe the

relationships between

length, area, and volume.

SPI 0706.4.3 Apply scale

factor to solve problems

involving area and volume.

Also addresses GLE 0706.2.3,

GLE 0706.4.1, SPI 0706.4.1.

Perimeter and Area

of Similar Figures

Suppose you double each dimension

5 in.

of the rectangle at the right. The new rectangle 4 in.

is similar to the original rectangle with a scale

factor of 2.

1. What is the perimeter of the original rectangle?


2. What is the perimeter of the new rectangle?


3. How is the perimeter of the new rectangle related to the perimeter
   of the original rectangle and the scale factor?

In similar figures, the perimeters are related by the scale factor. What

about area? Consider the rectangles from the Explore activity.

Original Rectangle New Rectangle

A = w A = w

A = 4 · 5 A = ( 2 · 4)( 2 · 5)

= ( 2 · 2 )(4 · 5)

= 22 (4 · 5)

The area of the new rectangle is equal to the area of the original

rectangle times the square of the scale factor.

Main Idea

Find the relationship

between perimeters

and areas of similar

figures.

The scale factor, 2, is

used as a factor twice.

Perimeter and Area of Similar Figures

Perimeter

Models

'JHVSF
"

a

Words If figure B is similar to figure A by a scale

factor, then the perimeter of B is equal to

the perimeter of A times the scale factor.

Symbols perimeter of figure B = perimeter of figure A · scale factor

Area

'JHVSF
#

b

Words If figure B is similar to figure A by a scale

factor, then the area of B is equal to the

area of A times the square of the scale

factor.

Symbols figure area of B = figure area of A · (scale factor)^2

Lesson 3B Similarity and Proportional Reasoning 299

293_303_C05_L3_895130.indd 299 12/29/09 1:10 PM