SOLUTION: The area of a hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. What is the length of a side of the regular hexagon? The answer must be in squar

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Question 300320: The area of a hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. What is the length of a side of the regular hexagon? The answer must be in square root form.
Answer by CharlesG2(834) About Me  (Show Source):
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The area of a hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. What is the length of a side of the regular hexagon? The answer must be in square root form.
perimeter equilateral triangle = 36 inches
length of side equilateral triangle = 36/3 = 12 inches
base of equilateral triangle = 12 inches
height equilateral triangle --> 12^2 - (12/2)^2 = h^2
144 - 6^2 = h^2
144 - 36 = 108 = h^2
h^2 = 108 = 3 * 36 = 3 * 6 * 6
h = 6sqrt(3)
area equilateral triangle = 1/2 * b * h = 6 * 6sqrt(3) = 36sqrt(3)
area of hexagon = 36sqrt(3)
area of 1/6 hexagon since hexagons are made of 6 equilateral triangles
area of 1/6 hexagon = 36sqrt(3) / 6 = 6sqrt(3)
if side of an equilateral triangle = 1, then perimeter of it would be 3,
height would be sqrt(1 - 1/4) or sqrt(3)/2 and area would be sqrt(3)/4
6sqrt(3) / (sqrt(3)/4 =
= 6sqrt(3) * 4/sqrt(3) = 24 --> this is the side of the hexagon squared
sqrt(24) = 2sqrt(6) = length of side of hexagon