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Area and perimeter of similar figures

# Area and perimeter of similar figures

The figures below are similar. The labeled sides are corresponding.

What is the perimeter of the smaller pentagon?

Remember that $\frac{a}{b}=\frac{P_1}{P_2}$ where $\frac{a}{b}$ is the ratio of the corresponding side lengths, and $\frac{P_1}{P_2}$ is the ratio of the perimeters.

Find the ratio of the corresponding side lengths.

$\frac{a}{b}=\frac{3}{9}=\frac{1}{3}$

Find the ratio of the perimeters.

$\frac{P_1}{P_2}=\frac{P_1}{45}$

Use these two ratios to set up a proportion and solve for P1.

$\frac{1}{3}$ = $\frac{P_1}{45}$

3
 P1
=
 1 × 45
Find the cross products

3
 P1
= 45 Simplify

3
 P1
÷ 3
=
 45 ÷ 3
Divide both sides by 3

 P1
= 15

The perimeter of the smaller pentagon is 15 centimeters.

The figures below are similar. The labeled sides are corresponding.

What is the area of the larger square?

Remember that $(\frac{a}{b})^2=\frac{A_1}{A_2}$ where $\frac{a}{b}$ is the ratio of the corresponding side lengths, and $\frac{A_1}{A_2}$ is the ratio of the areas.

Find the square of the ratio of the corresponding side lengths.

$(\frac{a}{b})^2=(\frac{7}{4})^2=\frac{49}{16}$

Find the ratio of the areas.

$\frac{A_1}{A_2}=\frac{A_1}{16}$

Use these two ratios to set up a proportion and solve for A1.

 $\frac{49}{16}$
=
 $\frac{A_1}{16}$

16
 A1
=
 49 × 16
Find the cross products

16
 A1
= 784 Simplify

16
 A1
÷ 16
=
 784 ÷ 16
Divide both sides by 16

 A1
= 49

The area of the larger square is 49 square feet.

The figures below are similar. The labeled sides are corresponding.
What is the perimeter of the larger triangle?
 14 in 56 in 40 in

P2 = in