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

Pentadecagon construction

A regular pentadecagon is constructible with straightedge and compass. The following animation illustrates 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.