Area of Regular Hexagon/Proof 2

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Theorem

Let $H$ be a regular hexagon.

Let the length of one side of $H$ be $s$.

Let $\AA$ be the area of $H$.


Then:

$\AA = \dfrac {3 \sqrt 3} 2 s^2$


Proof

A regular hexagon is a regular 6-sided polygon.

Therefore:

\(\ds \AA\) \(=\) \(\ds \dfrac 1 4 \times 6 \times s^2 \times \cot \dfrac \pi 6\) Area of Regular Polygon
\(\ds \) \(=\) \(\ds \dfrac 3 2 \times s^2 \times \sqrt 3\) Cotangent of $30 \degrees$
\(\ds \) \(=\) \(\ds \dfrac {3 \sqrt 3} 2 s^2\)

$\blacksquare$