document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #462068 by Cromlix(4381)\"\" \"About 
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If a equilateral triangle has a perimeter of
\n" ); document.write( "36 then it has 3 sides of 12ins each.
\n" ); document.write( "area of a triangle = 1/2(b*h)
\n" ); document.write( "The height will be found by creating a
\n" ); document.write( "line from the mid point of one of the
\n" ); document.write( "equilateral's sides up to the opposite
\n" ); document.write( "vertex of the triangle.
\n" ); document.write( "A right angled triangle is formed with
\n" ); document.write( "a side of 6ins. (1/2 base) and a hypotenuse
\n" ); document.write( "of 12ins.
\n" ); document.write( "12^2 - 6^2 = height^2
\n" ); document.write( "144 - 36 = height^2
\n" ); document.write( " height = square root of 108
\n" ); document.write( " height = 10.4ins.
\n" ); document.write( "Area of equilateral = 1/2(6*10.4)
\n" ); document.write( " = 31.2 ins^2
\n" ); document.write( "Area of regular hexagon = 3 root3/2 * x^2 (x = side)
\n" ); document.write( " 31.2 = 3 root 3/2 * x^2
\n" ); document.write( " 31.2/2.598 = x^2
\n" ); document.write( " 12 = x^2
\n" ); document.write( " x = root 12
\n" ); document.write( " x = 3.5ins.
\n" ); document.write( "Hope this helps.
\n" ); document.write( ":-) \n" ); document.write( "
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