Question

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 1

3a=36
a=12
area of equilateral triangle=36sqrt3
area of hexagon=(3 sqrt(3) s^2)/2
(3 sqrt(3) s^2)/2=36sqrt3
s^2=72/3=24
s=2sqrt6
\[side of hexagon=2\sqrt6\]