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

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

Pentadecagon construction

---

A regular pentadecagon is constructible with compass and straightedge. 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

პენტადეკაგონი