http://www.ck12.org Chapter 10. Perimeter and Area
10.7 Area and Perimeter of Similar Polygons
Here you’ll learn how to calculate the area and perimeter of similar polygons using ratios.
What if you wanted to create a scale drawing using scale factors? This technique takes a small object, like the
handprint below, divides it up into smaller squares and then blows up the individual squares. Either trace your hand
or stamp it on a piece of paper. Then, divide your hand into 9 squares, like the one to the right, probably 2in× 2 in.
Take a larger piece of paper and blow up each square to be 6in× 6 in(meaning you need at least an 18 in square
piece of paper). Once you have your 6in× 6 insquares drawn, use the proportions and area to draw in your enlarged
handprint. After completing this Concept, you’ll be able to explain the results of this technique.
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Click image to the left for more content.CK-12 Foundation: Chapter10AreaandPerimeterofSimilarPolygonsA
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Click image to the left for more content.Brightstorm:Similarity and AreaRatios
Guidance
Polygons are similar when the corresponding angles are equal and the corresponding sides are in the same proportion.
The scale factor for the sides of two similar polygons is the same as the ratio of the perimeters. In fact, the ratio of
any part of two similar shapes (diagonals, medians, midsegments, altitudes, etc.) is the same as the scale factor. The
ratio of the areas is thesquareof the scale factor. An easy way to remember this is to think about the units of area,
which are alwayssquared.Therefore, you would alwayssquarethe scale factor to get the ratio of the areas.
Area of Similar Polygons Theorem:If the scale factor of the sides of two similar polygons ismn, then the ratio of
the areas would be
(m
n) 2
.
Example A
The two rectangles below are similar. Find the scale factor and the ratio of the perimeters.
The scale factor is^1624 , which reduces to^23. The perimeter of the smaller rectangle is 52 units. The perimeter of the
larger rectangle is 78 units. The ratio of the perimeters is^5278 =^23.