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If a Square is touched on all sides...?
If a Square is touched on all sides by Equilateral Triangles, and there are four of said figures linked by lines to use the sides of 2 of the triangles on each figure to form a Dodecagon, What is the relationship of their relative areas?
1 Answer
- BattleaxeLv 78 years agoFavorite Answer
Area of the square = s^2
Area of each triangle = (1/2)bh where b = s
find h:
Divide each triangle into two right triangles.Since the triangles are equilateral, the hypotenuse = s and the base of each right triangle is s/2.
s^2 = (s/2)^2 + h^2
h^2 = s^2 - (s/2)^2
h = SQR(s^2 - (s/2)^2)
A(triangle) = (1/2)(s)(SQR(s^2 - (s/2)^2)
A(4 triangles) = (4)(1/2)(s)(SQR(s^2 - (s/2)^2) = 2s(SQR(s^2 - (s/2)^2)
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