# How to calculate ratio of areas of the shaded triangle and the hexagon?

How to calculate ratio of areas of the shaded triangle and the hexagon?

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## 1 Answer

Observe that the hexagon is equivalent to 6 equilateral triangles, and the shaded region is equivalent to such a triangle with double height.

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shaded triangle:hexagon == 2*1/6=1/3 =1:3 –  OM Loo Sep 16 '12 at 16:29
Is this the answareshaded triangle:hexagon == 1:3? –  OM Loo Sep 16 '12 at 16:30
@OMLoo: yes, it is –  enzotib Sep 16 '12 at 16:33
May I know the correct way to work out answer for triangle:hexagon ratio in this case? –  OM Loo Sep 17 '12 at 4:39
$A_{\text{hex}}=6A_{\text{eqtri}}$; $A_{\text{shad}}=2A_{\text{eqtri}}$; $r=A_{\text{shad}}/A_{\text{hex}}=(2A_{\text{eqtri}})/(6A_{\text{eqtri}})=1/3$ –  enzotib Sep 17 '12 at 10:21