SOLUTION: ABCDEF is a regular hexagon, and PQR is an equilateral triangle. What is the ratio of the area of the triangle to the area of the hexagon?

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Question 1170242: ABCDEF is a regular hexagon, and PQR is an equilateral triangle. What is the ratio of the area of the triangle to the area of the hexagon?
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Area of hexagon: A%5Bh%5D+=+%283sqrt%283%29%2F2%29%2Aa%5E2
For the triangle, A%5Bt%5D+=+%28sqrt%283%29%2F4%29%2A+a%5E2



A%5Bh%5D%2FA%5Bt%5D+=%283a%5E2sqrt%283%29%2F2%29%2F%28+a%5E2sqrt%283%29%2F4%29



A%5Bh%5D%2FA%5Bt%5D+=%283%2Fcross%282%291%29%2F%28+1%2Fcross%284%292%29

A%5Bh%5D%2FA%5Bt%5D+=3%2F2


Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The problem as stated can't be answered, because there is no information about the sizes of the triangle or hexagon.

The equilateral triangle could have a side length of 1 mile and the regular hexagon a side length of 1 inch; or vice versa....

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Note the solution from the other tutor assumes the side length of the triangle and hexagon are equal; then, assuming that, an arithmetic error leads to a wrong answer.

Indeed, if the side lengths are the same, the answer is easy, since the regular hexagon can be viewed as being composed of 6 equilateral triangles....