Nonagon

Regular nonagon (enneagon)
A regular nonagon (enneagon)
Type	Regular polygon
Edges and vertices	9
Schläfli symbol	{9}
Coxeter diagram
Symmetry group	Dihedral (D9), order 2×9
Internal angle (degrees)	140°
Dual polygon	Self
Properties	Convex, cyclic, equilateral, isogonal, isotoxal

In geometry, a nonagon /ˈnɒnəɡɒn/ (or enneagon /ˈɛniːəɡɒn/) is a nine-sided polygon or 9-gon.

The name "nonagon" is a prefix hybrid formation, from Latin (nonus, "ninth" + gonon), used equivalently, attested already in the 16th century in French nonogone and in English from the 17th century. The name "enneagon" comes from Greek enneagonon (εννεα, "nine" + γωνον (from γωνία = "corner")), and is arguably more correct, though somewhat less common than "nonagon".

A regular nonagon is represented by Schläfli symbol {9} and has internal angles of 140°. The area of a regular nonagon of side length a is given by

where the radius r of the inscribed circle of the regular nonagon is

and where R is the radius of its circumscribed circle:

Although a regular nonagon is not constructible with compass and straightedge (as 9 = 3², which is not a product of distinct Fermat primes), there are very old methods of construction that produce very close approximations.