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arlik [135]
3 years ago
6

What is the area of a hexagon with an apothem of 4 square root 3 ?

Mathematics
1 answer:
lidiya [134]3 years ago
7 0

A hexagon is six equilateral triangles; the apothem is the height of one of them.

The right triangle associated with that apothem has sides in ratio 1 : \sqrt{3}: 2 so the hypotenuse, which is the side of the equilateral triangle, is

s = \dfrac{2}{\sqrt{3}} (4 \sqrt{3}) = 8

so an area of a single triangle

A_\triangle = \frac 1 2 s h = 16 \sqrt{3}

The entire hexagon is six of these

A = 6(16 \sqrt{3}) = 96 \sqrt{3}

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