Pentadecagons

A pentadecagon is a polygon with fifteen sides and fifteen vertices. In a regular pentadecagon, all sides are equal in length, and all interior angles are equal. The sum of the interior angles of any pentadecagon, regular or irregular, is 2340 degrees.

The measure of each interior angle in a regular pentadecagon is 156 degrees. The measure of each exterior angle in a regular pentadecagon is 24 degrees. A regular pentadecagon can be constructed using a compass and straightedge, as 15 is a product of distinct Fermat primes (3 and 5). The area of a regular pentadecagon with side length 'a' can be calculated using the formula Area = (15/4) * a^2 * cot(pi/15).

The name "pentadecagon" is derived from Greek words, with "pentadeca" meaning fifteen and "gonia" meaning angle. In geometry, it is a specific example of a polygon.