Dodecagon

File:Dodecagon.svg

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

<math>\begin{align} A & = 3 \cot\left(\frac{\pi}{12} \right) a^2 =

                    3 \left(2+\sqrt{3} \right) a^2 \\
                & \approx 11{,}19615\,a^2.
\end{align}</math>

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

Perimeter

The perimeter of a regular dodecagon is

<math> \begin{align} P = 12s \end{align}</math>

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