Area of Regular Hexagon/Proof 1

Proof
From Regular Hexagon is composed of Equilateral Triangles, it follows that a regular hexagon can be dissected into six congruent equilateral triangles:


 * Regular Hexagon.svg

Let $\AA_T$ be the area of the bottom triangle.

Then by Area of Equilateral Triangle:


 * $ \AA_T = \dfrac{\sqrt 3} 4 s^2 $

As $H$ consists of six congruent triangles, it follows that:


 * $ \AA = 6\AA_T = \dfrac{6\sqrt 3} 4 s^2 = \dfrac{3\sqrt3} 2 s^2 $