Question 1111765
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.

side of triangle = {{{(sqrt(3)/4)*s^2}}}

perimeter = 36 so side = 12in  12^2=144

Area = {{{(sqrt(3)/4)*144}}}

Area = {{{36*sqrt(3)}}}

Area of hexagon = {{{36sqrt(3)}}}

Area of hexagon = {{{(sqrt(3)/4)*s^2 *6}}} s= length of side

{{{36*sqrt(3)}}}= {{{(sqrt(3)/4)*s^2 *6}}}

{{{s^2=24}}}

s={{{2sqrt(6)}}}