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The triangles below are similar. Find the ratio (larger to smaller) of their perimeters and of their areas.

5 4. From larger to smaller, the similarity ratio is . By the Perimeters and Areas of Similar Figures Theorem, the ratio of the perimeters is also , and the ratio of the areas is , or . 5 4. 25 16. 5 2 4 2. Perimeters and Areas of Similar Figures. LESSON 10-4.

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The triangles below are similar. Find the ratio (larger to smaller) of their perimeters and of their areas.

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  1. 5 4 From larger to smaller, the similarity ratio is . By the Perimeters and Areas of Similar Figures Theorem, the ratio of the perimeters is also , and the ratio of the areas is , or . 5 4 25 16 52 42 Perimeters and Areas of Similar Figures LESSON 10-4 Additional Examples The triangles below are similar. Find the ratio (larger to smaller) of their perimeters and of their areas. The shortest side of the triangle to the left has length 4, and the shortest side of the triangle to the right has length 5. Quick Check

  2. Because the ratio of the lengths of the corresponding sides of the regular octagons is , the ratio of their areas is , or . 8 3 82 32 64 9 64 9 320 A = Write a proportion. 64A = 2880 Use the Cross-Product Property. A = 45 Divide each side by 64. Perimeters and Areas of Similar Figures LESSON 10-4 Additional Examples The ratio of the lengths of the corresponding sides of two regular octagons is . The area of the larger octagon is 320 ft2. Find the area of the smaller octagon. 8 3 All regular octagons are similar. The area of the smaller octagon is 45 ft2. Quick Check

  3. Perimeters and Areas of Similar Figures LESSON 10-4 Additional Examples Benita plants the same crop in two rectangular fields each with side lengths in a ration 2:3. 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. Quick Check

  4. Find the similarity ratio a : b. 32 72 a2 b2 a2 b2 = The ratio of the areas is a2 : b2. 16 36 = Simplify. a b 4 6 2 3 = = Take the square root. Perimeters and Areas of Similar Figures LESSON 10-4 Additional Examples The areas of two similar pentagons are 32 in.2 and 72 in.2 What is their similarity ratio? What is the ratio of their perimeters? The similarity ratio is 2 : 3. By the Perimeters and Areas of Similar Figures Theorem, the ratio of the perimeters is also 2 : 3. Quick Check

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