Nsided

Nsided is an adjective used in geometry to describe a polygon with n sides, where n is a positive integer. In ordinary Euclidean geometry, n is at least 3; degenerate cases with fewer sides are sometimes considered in broader contexts. The term is commonly written as n-sided or n-gonal and is used as a general descriptor for any polygon, regardless of its shape.

The most familiar nsided shapes are triangles (n = 3), quadrilaterals (n = 4), pentagons (n = 5), and hexagons (n = 6). When all sides and all angles are equal, the figure is a regular n-gon; otherwise it is irregular. An nsided polygon has exactly n vertices and n edges. The sum of its interior angles is 180(n − 2) degrees. For convex polygons, each interior angle is less than 180 degrees.

For a regular nsided polygon, several formulas express area in terms of side length or circumradius. If the side length is a, the area is A = (n a^2) / (4 tan(π/n)) or equivalently A = (1/4) n a^2 cot(π/n). If the circumradius is R, the area is A = (1/2) n R^2 sin(2π/n).

Nsided polygons appear in a variety of mathematical contexts, including tiling problems, polygonal-number sequences, and computer graphics, where the value of n determines symmetry, tiling properties, and ease of computation.