2.6: Perimeters and Areas of Similar

Figures

Perimeters of Similar Figures

When two figures are similar: The ratio of their

perimeters is equal to the ratio of their corresponding side lengths.

Finding the Ratios of Perimeters

The ratio of the perimeters is

Find the ratio (red to blue) of the perimeters of the similar rectangles.

2

3

Areas of Similar Figures

When two figures are similar: The ratio of their areas is

equal to the square of the ratio of their corresponding side lengths.

Finding Ratios of Areas

The ratio of the areas is

Find the ratio (red to blue) of the areas of the similar triangles.

9

25

Using Proportions to Find Perimeters and Areas

The rectangular pool and the court are similar. So, use the ratio of corresponding side lengths to write and solve proportions to find the perimeter and area of the pool.

A swimming pool is similar in shape to a volleyball court. Find the perimeter P and the area A of the pool.

Lesson 2.6: Perimeters and Areas of similar FiguresEssential Question: How do changes in side length of similar figures affect the perimeters and areas of the figures?

EX 6

Determine the ratio (green to blue) of perimeters of the similar rectangles.

10

9

15

3

2

48

32

blue

greenThe ratio of perimeters is 2/3.

RATIO OF SIDES:

3

2

9

6

RATIO of sides is same as perimeter

P = 32 P =

48

You Try it: 3

56

10

Find the ratio (yellow to blue) of the perimeters.Yellow perimeter16

Blue perimeter

32Ratio of Perimeters

2

1

32

16

LEFT COLUMN QUESTION

How are ratio of perimeters and ratio of side lengths related on similar figures?

Answer: Ratios of perimeters is the SAME as ratio of sides of similar figures.

Area of similar figuresDetermine the ratio of sides and areas (blue

to green) of the following figures

3

6

2

4

RATIO OF SIDES:

2

3

AREAS

BLUE 18

GREEN 8

RATIO OF AREAS

4

9

8

18

Compare the relationship between the two ratios.

(They are not the same)

The ratio of sides squared is the ratio of areas

YOU TRY IT:Find the ratio of the areas of the two similar figures (Red to Blue).

610RATIO OF

SIDES

5

3

3 5 AREAS bh2

1

RED 9

Blue 25 RATIO OF AREAS

25

9

LEFT COLLUMN How are the ratio of sides compared to the ratio of areas?QUESTION: Answer: When figures are similar, the ratio of areas is the square of the ratio of sides.

The two figures are similar. Find the ratios (shaded to nonshaded) of the perimeters and of the areas.

Ratio of Perimeters: 5

3

10

6

Ratio of Areas: 25

9

5

32