# How do you find the area of a given hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches?

May 27, 2015

Warning: I suspect there is something wrong in the statement of this question; however....

If the perimeter of an equilateral triangle is 36 inches, each side is 12 inches and by the Pythagorean Theorem the height is $\sqrt{{12}^{2} - {6}^{2}} = \sqrt{108} = 6 \sqrt{3}$

The area of the triangle is
$A = \frac{1}{2} b h$

$= \frac{1}{2} \cdot 12 \cdot 6 \sqrt{3} \text{square inches}$

$= 36 \sqrt{3} \text{square inches}$