Elevensided

Elevensided denotes a polygon having eleven sides. In geometry, the term is commonly replaced by hendecagon or undecagon, with "elevensided" being a less common descriptive form. The hendecagon name derives from Greek hendeka "eleven" and gonia "angle"; undecagon combines Latin undecem "eleven" with -gon.

In any polygon with n sides, the sum of interior angles is (n−2)×180 degrees. For an elevensided polygon, this sum is 9×180 = 1620 degrees. A regular elevensided polygon, in which all sides and all interior angles are equal, has each interior angle equal to 1620/11 ≈ 147.27 degrees, and each exterior angle equal to 360/11 ≈ 32.73 degrees. The central angle between adjacent vertices in a regular such polygon is also 360/11 degrees.

Construction notes: A perfect regular hendecagon is not constructible with straightedge and compass, since 11 is not a product of a power of two and distinct Fermat primes. Consequently, exact classical constructions rely on approximate methods or non-classical tools.

Variations: An elevensided polygon need not be regular; side lengths and angles may vary, though the total interior angle sum remains fixed at 1620 degrees. The term is typically used in descriptive contexts rather than formal proofs.

See also: hendecagon; undecagon; polygon.