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A decagon is a ten-sided polygon. It has ten vertices and ten edges. The sum of the interior angles of any decagon is 1440 degrees. If a decagon is regular, all its sides are of equal length, and all its interior angles are equal. In a regular decagon, each interior angle measures 144 degrees, and each exterior angle measures 36 degrees.

The area of a regular decagon with side length 's' can be calculated using the formula A = (5/2) * s^2 * cot(pi/10), or approximately A = 7.694 * s^2. The radius of the circumcircle of a regular decagon with side length 's' is R = (s/2) * csc(pi/10), and the radius of the inscribed circle (apothem) is r = (s/2) * cot(pi/10).

Decagons appear in various contexts, though less frequently than polygons with fewer sides. For example, the United States' ten-cent coin, the dime, features a decagonal shape in its design, with the profile of Franklin D. Roosevelt inscribed on one side and an olive branch, torch, and oak branch on the other. In architecture, decagonal elements can sometimes be found in decorative patterns or structural designs, adding a less common geometric complexity. The construction of a regular decagon is possible using a straightedge and compass, though it is not as straightforward as constructing a square or a hexagon.