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 $30 \degrees$ | |||||||||||
\(\ds \) | \(=\) | \(\ds \dfrac {3 \sqrt 3} 2 s^2\) |
$\blacksquare$