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

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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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    $A_{\text{hex}}=6A_{\text{eqtri}}$; $A_{\text{shad}}=2A_{\text{eqtri}}$; $r=A_{\text{shad}}/A_{\text{hex}}=(2A_{\text{eqtri}})/(6A_{\text{eqtri}})=1/3$2012-09-17