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27 September, 15:18

The area of a regular hexagon is 55 in^2. Find the length of a side. Round your answer to the nearest tenth. I know the answer is 4.6 in., but I have no idea how to solve it.

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  1. 27 September, 15:32
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    Polygon area = n*side length^2 / [4*tan (180/n) ]

    side length^2 = polygon area * [4*tan (180/n) ] / n

    where n is the number of sides

    side length^2 = 55 sq inches * (4*tan (180/6)) / 6

    side length^2 = 55 sq inches * 4 * tan (30) / 6

    side length^2 = (55 sq inches * 4 * 0.57735) / 6

    side length^2 = 127.017 / 6

    side length^2 = 21.1695

    side length = square root (21.1695)

    side length = 4.6010324928
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