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Geometry Area of Two Similar Triangle
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Area of Two Similar Triangle
To find the ratio of the areas of similar triangles, just square the similarity ratio. The ratio of the perimeters on the other hand equals the similarity ratio.
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Example: Prove that the area of the equilateral triangle described on the side of a square is half the area of the equilateral triangle described on its diagonal.
Solution: A square ABCD. Equilateral triangles BCE and ACF have been described on side BC and diagonal AC respectively.         ...[Given]
You have to Prove: Area (BCE) = 1/2. Area (ACF)
Since BCE and ACF are equilateral.
There­fore, they are equiangular (each angle being equal to 60)
and hence
Area of (BCE) / Area of (ACF) = BC2 / AC2
Area of (BCE) / Area of (ACF) = BC2 / (2 BC)2
Area of (BCE) / Area of (ACF) = 1/2
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