Lesson 2.6: Perimeters and Areas of similar Figures

Essential Question: How do changes in side length of similar figures affect the perimeters and areas of the figures?

EX6

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 = 32P = 48

You Try it:3

56

10Find the ratio (yellow to blue) of the perimeters.

Yellow perimeter 16

Blue perimeter 32

Ratio 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 figures

Determine 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 AREAS4

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).

610

RATIO 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