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

The figures below are two regular pentagons. Their similarity ratio is 8 4 Their similarity ratio is 8:4 or 2:1.

Use the Similarity Ratio to Find Area and Perimeter Find the perimeter and Area of the similar figures. 1. Find the similarity ratio: Ratio of 2/3 a=2 and b=3 2. Use theorem to find perimeter and area 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 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. 4 = 2 10 5 1. Find ratio of lengths of corresponding sides. The area is 22 52 = 4 25 2. Write a proportion and solve. 4 = 27.5 25 A 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: The area is a2 b2 = 50 98 = 25 49 2. Simplify a b = 5 Take square root of both sides 7

Real-world and Similarity Ratios 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? 1 2 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.