area of a hexagon is equal to the area of an equilateral triangle

Question

The area of a 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

The perimeter of equilateral triangle = 3s = 36 where s = side

                                                        => s = 36/3 = 12 inches

Area of equilateral triangle = (1/2 *s)^2*√3

                                           = (s^2/4)√3

                                           = √3 s^2 / 4

                                           = √3 (12^2) /4

                                           = 36√3 inches^2

Area of hexagon = 3√3 / 2 * s^2

Given that Area of equilateral triangle = Area of hexagon

=> 36√3 = 3√3 /2 *s^2

=> 2*36√3 / 3√3 = s^2

=> s^2 = 24

=> s = 2√6 inches

Therefore length of a side of regular hexagon is 2√6 inches.