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A regular hexagon and an equilateral triangle have equal perimeters... What is the ratio of their areas?
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- ?Lv 76 years ago
Let s = one side of the ∆. Then P = 3s,
and its area is (√3)s^2 / 4
Since the perimeter of the hexagon is also 3s,
each side is s/2. Using the area formula for
a regular hexagon, A = (3√3)(s/2)^2 / 2
= (3√3)s^2 / 8. So the ratio of hexagon area
to triangle area is [ (3√3)s^2 / 8 ] / [ (√3)s^2 / 4 ]
= 3/2, or 3 : 2
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