hectogon

A hectogon is a polygon with 100 sides and 100 vertices. The term is derived from the Greek word "hekaton" meaning one hundred and "gonia" meaning angle. Like any polygon, a hectogon can be convex or concave, regular or irregular. A regular hectogon has all sides of equal length and all interior angles equal. The measure of each interior angle in a regular hectogon can be calculated using the formula (n-2) * 180 / n, where n is the number of sides. For a hectogon, this would be (100-2) * 180 / 100 = 98 * 1.8 = 176.4 degrees. The sum of the interior angles of any hectogon is (100-2) * 180 = 17640 degrees. The number of diagonals in a hectogon is given by the formula n(n-3)/2, which for n=100 is 100(100-3)/2 = 100 * 97 / 2 = 4850. Due to the large number of sides, hectogons are rarely encountered in practical geometry and are primarily theoretical constructs. In some contexts, the term "hectangle" might be used to refer to a specific type of hectogon, though this is not standard terminology.