Presentation on theme: "Section 8-6 Perimeter and Area of Similar Figures SPI 22d: determine the perimeter & area given the ratio of 2 similar polygons."— Presentation transcript:
1 Section 8-6 Perimeter and Area of Similar Figures SPI 22d: determine the perimeter & area given the ratio of 2 similar polygonsObjectives:find area and perimeter of similar figures
2 The figures below are two regular pentagons. Their similarity ratio is 84Their similarity ratio is8:4 or 2:1.
3 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 2/3a=2 and b=32. Use theorem to find perimeter and areaBy the Theorem:Ratio of perimeter (small to large) is 2/3.Ratio of area (small to large) is 4/9.
4 Use the Similarity Ratio to Find Area and Perimeter These two rhombi are similar. Their ratio of similarity is3 : 1. Find x.Set up RatioSolve Proportion3x = 12x = 4
5 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 = 21. Find ratio of lengths of corresponding sides.The area is 2252= 4252. Write a proportion and solve.4 = 27.5A4A = (25)(27.5)A =
6 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 a2b2= 5098= 25492. Simplifyab= Take square root of both sides7
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?12The 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 : 1.Because seeding the smaller field costs $8, seeding times as much land costs 12.25($8).Seeding the larger field costs $98.