Section 8-6 Perimeter and Area of Similar Figures SPI 22d: determine the perimeter & area given the ratio of 2 similar polygons

Objectives:• find area and perimeter of similar figures

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Similarity Ratio

Ratio of 2/3 a=2 and b=3

By the Theorem: Ratio of perimeter (small to large) is 2/3. Ratio of area (small to large) is 4/9.

Use the Similarity Ratio to Find Area and Perimeter

Find the perimeter and Area of the similar figures.

1. Find the similarity ratio:

2. Use theorem to find perimeter and area

Use the Similarity Ratio to Find Area and Perimeter

These  two rhombi are similar.  Their ratio of similarity is 3 : 1. Find x.

Set up Ratio Solve Proportion

3x = 12 x = 4

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

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?

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Real-world and Similarity Ratios