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10.4 Perimeters and Areas of Similar Figures

10.4 Perimeters and Areas of Similar 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. Ex 1: The trapezoids are Similar. Find the similarity ratio (of the top shape to the bottom shape)

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10.4 Perimeters and Areas of Similar Figures

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  1. 10.4 Perimeters and Areas ofSimilar Figures

  2. Perimeters and Areas of Similar Figures • If the similarity ratio is , then: • The ratio of the perimeters is • The ratio of the areas is

  3. 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)

  4. Ex 1:The trapezoids are Similar • Find the similarity ratio • Find the perimeter ratio • Find the area ratio

  5. Ex 1:The trapezoids are Similar • Find the similarity ratio • Find the perimeter ratio • Find the area ratio

  6. Ex 1:The trapezoids are Similar • Find the similarity ratio • Find the perimeter ratio • Find the area ratio

  7. 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?

  8. 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?

  9. 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

  10. 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:

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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.

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