11gon

An 11-gon is a polygon with eleven sides and eleven angles. It is also known as a hendecagon. Like any polygon, the sum of the interior angles of an 11-gon can be calculated using the formula (n-2) * 180 degrees, where n is the number of sides. For an 11-gon, this sum is (11-2) * 180 = 9 * 180 = 1620 degrees.

A regular 11-gon has all eleven sides of equal length and all eleven interior angles equal in measure. In a regular 11-gon, each interior angle measures 1620 / 11 degrees, which is approximately 147.27 degrees. The exterior angles of any convex polygon sum to 360 degrees. Therefore, each exterior angle of a regular 11-gon measures 360 / 11 degrees, approximately 32.73 degrees.

The construction of a regular 11-gon using only a compass and straightedge is not possible. This is because 11 is a prime number that is not a Fermat prime. Constructible polygons have a number of sides that is a product of a power of two and distinct Fermat primes.

In geometry, an 11-gon can be inscribed in a circle, forming a cyclic 11-gon, or it can be tangential to a circle, forming a tangential 11-gon. The properties and formulas related to area and perimeter will differ depending on whether the 11-gon is regular or irregular.