Pentadecagon

From Freepedia

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

<math>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.</math>

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.

Polygons
Triangle | Quadrilateral | Pentagon | Hexagon | Heptagon (Septagon) | Octagon | Enneagon (Nonagon) | Decagon | Hendecagon | Dodecagon | Triskaidecagon | Pentadecagon | Heptadecagon | Enneadecagon | Icosagon | Tricontagon | Pentacontagon | Hectagon | Chiliagon | Myriagon