octodecagon

An octodecagon is a polygon with eighteen sides and eighteen vertices. In a regular octodecagon, all sides are of equal length and all interior angles are equal. The sum of the interior angles of any octodecagon, whether regular or irregular, is calculated by the formula (n-2) * 180 degrees, where n is the number of sides. For an octodecagon, this is (18-2) * 180 = 16 * 180 = 2880 degrees.

The measure of each interior angle in a regular octodecagon is 2880 / 18 = 160 degrees. The exterior angle of a regular octodecagon measures 360 / 18 = 20 degrees. The number of diagonals in an octodecagon can be found using the formula n(n-3)/2, which for n=18 is 18(18-3)/2 = 18 * 15 / 2 = 135 diagonals.

The area of a regular octodecagon with side length 'a' can be calculated using the formula A = (18/4) * a^2 * cot(pi/18), which simplifies to A = (9/2) * a^2 * cot(10 degrees). The construction of a regular octodecagon is possible with a compass and straightedge, as 18 can be factored into 2 * 3^2, and 3 is a Fermat prime.