Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

enter image description here

share|cite|improve this question

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

share|cite|improve this answer
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

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.