Pentadecagon

Template:Regular polygon db A pentadecagon or quindecagon or 15-gon is a shape with 15 sides and 15 corners.

Regular pentadecagon

All sides of a regular pentadecagon are the same length. Each corner is 156°. All corners added together equal 2340°.

Area

The amount of space a regular pentadecagon takes up is

$\begin{array}{cc}A=\frac{15}{4}{a}^2\cot \frac{\pi }{15}& =\frac{15}{4}\sqrt{7+2\sqrt{5}+2\sqrt{15+6\sqrt{5}}}{a}^2\\ & =\frac{15a^2}{8}(\sqrt{3}+\sqrt{15}+\sqrt{2}\sqrt{5+\sqrt{5}})\\ & \simeq 17.6424a^2.\end{array}$

a is the length of one of its sides.

Uses

A regular triangle, decagon, and pentadecagon can completely fill a plane vertex.

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