10.4 Perimeters and Areas ofSimilar Figures

Perimeters and Areas of Similar Figures

If the similarity ratio is , then:

The ratio of the perimeters is

The ratio of the areas is

a

b

a

b

a2

b2

Ex 1:The trapezoids are Similar

Find the similarity ratio(of the top shape to the bottom shape)

Find the perimeter ratio(of the top shape to the bottom shape)

Find the area ratio(of the top shape to the bottom shape) 6 m

9 m

Ex 1:The trapezoids are Similar

Find the similarity ratio

Find the perimeter ratio

Find the area ratio6 m

9 m

9

6 =

3

2

Ex 1:The trapezoids are Similar

Find the similarity ratio

Find the perimeter ratio

Find the area ratio6 m

9 m

9

6 =

3

2

3

2

Ex 1:The trapezoids are Similar

Find the similarity ratio

Find the perimeter ratio

Find the area ratio6 m

9 m

9

6 =

3

2

3

2

9

4

Ex 2:

Two similar polygons have corresponding sides in the ratio of 5:7

What is the ratio of the perimeters?

What is the ratio of the areas?

Ex 2:

Two similar polygons have corresponding sides in the ratio of 5:7

What is the ratio of the perimeters?5:7

What is the ratio of the areas?

Ex 2:

Two similar polygons have corresponding sides in the ratio of 5:7

What is the ratio of the perimeters?5:7

What is the ratio of the areas? 25:49

Example 3 The similarity ratio of 2 triangles is

3:2. The area of the larger triangle is 36cm2. Find the area of the smaller triangle.

What is the ratio of the areas? Set up the proportion:

Ex 4: The two regular pentagonsare similar

The area of the smaller pentagon is 42.3 cm. What is the area of the larger pentagon

4 cm

10 cm

25

4 =

x

42.3

x = 264.375 cm2

Finding Area using Similar Figures

The area of the small pentagon is about 27.5 cm sq. Find the area of the larger pentagon.

1. Find ratio of lengths of corresponding sides.

2. Write a proportion and solve. 4 = 27.525 A

4 = 210 5

The area is 22

52

= 4 25

4A = (25)(27.5) A = 171.875

Ex 6:

The area of two triangles are 75 square meters and 12 square meters.

What is the similarity ratio

What is the perimeter ratio

Finding Similarity and Perimeter Ratios

The areas of two similar triangles are 50 cm2 and 98cm2. a. What is the similarity ratio?

b. What is the ratio of their perimeters?

1. Find the similarity ratio:

2. Simplify

= 25 49

The area is a2

b2

= 50 98

= 5 Take square root of both sides 7

ab

The similarity ratio of the fields is 3.5 : 1, so the ratio of the areas of the fields is (3.5)2 : (1)2, or 12.25 : 1.

Because seeding the smaller field costs $8, seeding 12.25 times as much land costs 12.25($8).

Seeding the larger field costs $98.

Benita plants the same crop in two rectangular

fields. Each dimension of the larger field is 3

times the dimension of the smaller field. Seeding

the smaller field costs $8. How much money does

seeding the larger field cost?

12

Real-world and Similarity Ratios