Dodecagon

A dodecagon

A dodecagon or 12-gon is a shape with 12 sides and 12 corners.

Regular dodecagon

All sides of a regular dodecagon are the same length. Each corner is 150°. All corners added together equal 1800°.

Area

The amount of space a regular dodecagon takes up is

${\begin{aligned}A&=3\cot \left({\frac {\pi }{12}}\right)a^{2}=3\left(2+{\sqrt {3}}\right)a^{2}\\&\approx 11{,}19615\,a^{2}.\end{aligned}}$

The variable A represents the area, and the variable a represents the apothem.

Perimeter

The perimeter of a regular dodecagon is

${\begin{aligned}P=12s\end{aligned}}$

The variable P represents the perimeter, and the variable s represents one side.