Perimeter and Area of Similar Figures

GeometryUnit 4, Lesson 4

Perimeters of Similar Figures http://

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Areas of Similar Figures http://

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What we discovered: If the similarity ratio of two similar

figures is a:b, then The ratio of their perimeters is a:b The ratio of their areas is a2:b2

Example 1

The area of the smaller regular hexagon is 30 in2. Find the area of the larger hexagon.1.What is the ratio of the corresponding sides?

2.What is the ratio of the areas?

3 in 5 in

5

3

25

9

Example 1

The area of the smaller regular hexagon is 30 in2. Find the area of the larger hexagon.

3 in 5 in

x

30

25

9

7509 x9 9

3.83x

Example:

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:

4

9

x

36

4

9

1449 x16x

Example:

The areas of two similar triangles are 50cm2 and 98cm2. What is the ratio of their perimeters?

Simplify the ratio then Work Backwards!

Example 50

98 REDUCE! 25

49 Find the square root 5

7

Example:

The areas of two similar rectangles are 2940 ft2 and 135 ft2. Find the ratios to their perimeters.

Ratio = 14/3