Area Ratios of similar figures Polygons are similar

Area Ratios of similar figures Polygons are similar if they have the same shape, but differ in size. We use a scale factor or similarity ratio to describe their difference in size.

Theorem 87 -1 • • If 2 similar figures have a scale factor of a: b, then the ratio of their perimeters is a: b, and the ratio of their areas is a 2 : b 2

Draw 2 similar triangles, one with a base of b and a height of h and a second with a base of 2 b and a height of 2 h. • Find the area of each and determine their area ratio. •

practice • Find the ratios of the perimeters and the ratios of the areas of these 2 similar triangles 15 10

Ratios of perimeters of similar figures • Find the perimeter of the smaller rectangle if the perimeter of the larger is 60 ft. 5 x 2 x

Ratios of areas of similar figures. • If the 2 triangles have a similarity ratio of 2: 5, determine the ratio of their areas and the area of the smaller triangle. 40 cm. 25 cm.

practice • • 1. You are given 2 similar hexagons, and the perimeter of the large hexagon is 120 feet, and each side of the smaller hexagon is 1. 5 feet. Find the perimeter of the small hexagon. 2. In the following similar parallelograms, find the ratio of their areas and the area of the larger parallelogram. 8 cm. 6 cm. 10 cm. 50 cm.

practice • 3. The kitchen on a floor plan shows a triangle from the sink to the refrigerator to the counter that has an area of 1. 5 square feet. If the floor plan has a scale factor of 1: 10, what will be the actual area of this triangle when the house is built?