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The area of a given hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. Find the length of a side of the regular hexagon.

Mathematics
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hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. Find the length of a side of the regular hexagon. equilateral triangle perimeter 36 inches each side eq. triangle then 12 inches height eq. triangle = sqrt(12^2 - (1/2*12)^2) = sqrt(144 - 6^2) height eq. triangle = sqrt(144 - 36) = sqrt(108) height = sqrt(36*3) = 6sqrt(3) area eq. triangle = 1/2 * base * height = 1/2 * 12 * 6sqrt(3) area eq. triangle = 36sqrt(3) ( area of an equilateral triangle = side^2 * sqrt(3)/4 36sqrt(3) * 4/sqrt(3) = side^2 144 = side^2 12 = side as stated above ) hexagon area = 36sqrt(3) hexagon is made of 6 equilateral triangles each with 6sqrt(3) as their area (6 * 6sqrt(3) = 36sqrt(3) hexagon eq. triangle area = 6sqrt(3) 6sqrt(3) = side^2 * sqrt(3)/4 6sqrt(3) * 4/sqrt(3) = 24 = side^2 2sqrt(6) = side = length of the side of the regular hexagon This one is lengthy so be mindful this is an example. Hope it helps Brittney (:
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