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

Question

enter image description here

enzotib · Answer 1 · 2012-09-15 16:22:49Z

up vote 7 down vote

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

answered Sep 15 '12 at 16:22

enzotib
2,211415

	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

1 Answer