pentadecagon

In geometry, a pentadecagon is any 15-sided, 15-angled, polygon. A regular pentadecagon has interior angles of 156, and with a side length a, has an area given by

A=\frac{15}{4}a^2 \cot \frac{\pi}{15} = \frac{15a^2}{8} \left( \sqrt{3}+\sqrt{15}+\sqrt{2}\sqrt{5+\sqrt{5}} \right) \simeq 17.6424a^2.

Pentadecagon construction

A regular pentadecagon is constructible with straightedge and compass. The following animation illistrates this process in 36 steps, and is adapted from a method given in Euclid's Elements, Book IV, Proposition 16. Note that the compass radius remains unaltered during steps 14 through 21.

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