12gon

A 12gon is a polygon with twelve sides and twelve angles. It is also known as a dodecagon. In a regular dodecagon, all sides are of equal length and all interior angles are equal. The interior angle of a regular dodecagon can be calculated using the formula (n-2) * 180 / n, where n is the number of sides. For a dodecagon, this means (12-2) * 180 / 12 = 10 * 180 / 12 = 1800 / 12 = 150 degrees. The sum of the interior angles of any dodecagon, regular or irregular, is always 1800 degrees.

The area of a regular dodecagon can be calculated in several ways. One common formula involves the side length 's' and is given by the expression 3 * (2 + sqrt(3)) * s^2. Another method uses the apothem 'a' (the distance from the center to the midpoint of a side), with the area being 12 * a * s / 2, which simplifies to 6 * a * s. The perimeter of a regular dodecagon is simply 12 times its side length.

Dodecagons appear in various contexts. For example, the British 12-sided coin, introduced in 1982, is a prominent example of a dodecagonal shape in everyday currency. In geometry, dodecagons are studied as part of the broader family of polygons, exploring their properties and relationships with other geometric figures. Their symmetrical properties make them interesting subjects in tessellations and geometric constructions.