SOLUTION: 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.

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Question 759523: 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.
Answer by Cromlix(4381) (Show Source):
You can put this solution on YOUR website!
If a equilateral triangle has a perimeter of
36 then it has 3 sides of 12ins each.
area of a triangle = 1/2(b*h)
The height will be found by creating a
line from the mid point of one of the
equilateral's sides up to the opposite
vertex of the triangle.
A right angled triangle is formed with
a side of 6ins. (1/2 base) and a hypotenuse
of 12ins.
12^2 - 6^2 = height^2
144 - 36 = height^2
height = square root of 108
height = 10.4ins.
Area of equilateral = 1/2(6*10.4)
= 31.2 ins^2
Area of regular hexagon = 3 root3/2 * x^2 (x = side)
31.2 = 3 root 3/2 * x^2
31.2/2.598 = x^2
12 = x^2
x = root 12
x = 3.5ins.
Hope this helps.
:-)