document.write( "Question 312449: 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 #223362 by CharlesG2(834)\"\" \"About 
You can put this solution on YOUR website!
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.\r
\n" ); document.write( "\n" ); document.write( "equilateral triangle perimeter 36 inches
\n" ); document.write( "each side eq. triangle then 12 inches
\n" ); document.write( "height eq. triangle = sqrt(12^2 - (1/2*12)^2) = sqrt(144 - 6^2)
\n" ); document.write( "height eq. triangle = sqrt(144 - 36) = sqrt(108)
\n" ); document.write( "height = sqrt(36*3) = 6sqrt(3)
\n" ); document.write( "area eq. triangle = 1/2 * base * height = 1/2 * 12 * 6sqrt(3)
\n" ); document.write( "area eq. triangle = 36sqrt(3)
\n" ); document.write( "( area of an equilateral triangle = side^2 * sqrt(3)/4
\n" ); document.write( "36sqrt(3) * 4/sqrt(3) = side^2
\n" ); document.write( "144 = side^2
\n" ); document.write( "12 = side as stated above )
\n" ); document.write( "hexagon area = 36sqrt(3)
\n" ); document.write( "hexagon is made of 6 equilateral triangles each with 6sqrt(3) as their area
\n" ); document.write( "(6 * 6sqrt(3) = 36sqrt(3)
\n" ); document.write( "hexagon eq. triangle area = 6sqrt(3)
\n" ); document.write( "6sqrt(3) = side^2 * sqrt(3)/4
\n" ); document.write( "6sqrt(3) * 4/sqrt(3) = 24 = side^2
\n" ); document.write( "2sqrt(6) = side = length of the side of the regular hexagon
\n" ); document.write( " \n" ); document.write( "
\n" );