sexdecagon

A sexdecagon is a polygon with sixteen sides and sixteen vertices. In a regular sexdecagon, all sides are of equal length and all interior angles are equal. The sum of the interior angles of any sexdecagon, regular or irregular, is 2520 degrees. For a regular sexdecagon, each interior angle measures 157.5 degrees. The exterior angle of a regular sexdecagon is 22.5 degrees.

The formula for calculating the interior angle of a regular n-sided polygon is (n-2) * 180 / n. For a sexdecagon, n=16, so the interior angle is (16-2) * 180 / 16 = 14 * 180 / 16 = 2520 / 16 = 157.5 degrees. The formula for the area of a regular sexdecagon with side length 's' is 4 * (1 + sqrt(2) + sqrt(4 + 2*sqrt(2))) * s^2.

Sexdecagons are relatively uncommon in everyday geometry compared to shapes like squares or hexagons. However, they can appear in more complex geometric constructions or theoretical discussions. The construction of a regular sexdecagon is possible with a compass and straightedge, as 16 is a power of 2 (2^4). This means it can be constructed by repeatedly bisecting the angle of a square.