8.6:Perimeters and Areas of Similar Figures

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8.6:Perimeters and Areas of Similar Figures
Objective: To find the perimeters and areas of similar figures

Theorem: If the similarity ratio of 2 similar figures is a:b, then:
The ratio of their perimeters is a : b The ratio of their areas is a2: b2 (square the similarity ratio)

The following trapezoids are similar.
Find the ratio of the perimeters: Find the ratio of the areas (larger to smaller): 9 m 6 m

Two similar polygons have corresponding sides in the ratio 5:7.
Find the ratio of their perimeters. Find the ratio of their areas.

When you know the area of one of the 2 similar polygons, you can use a proportion to find the area of the other polygon. Two pentagons are similar. The area of the smaller pentagon is about 27.5 cm2. Find the area, A, of the larger regular pentagon. Ratio of the areas: Set up proportion: 4 cm 10 cm

Find Similarity and Perimeter Ratios
The areas of 2 similar triangles are 50 cm2 and 98 cm2. What is the similarity ratio? Ratio of their perimeters? Ratio of areas: Simplify, if possible: Take square root of both sides: