In geometry, a decagon is any polygon with ten sides and ten angles, and usually refers to a regular decagon, having all sides of equal length and each internal angle equal to 144°. Its Schläfli symbol is {10}.

The area of a regular decagon is: (with t = edge length)

An alternative formula is Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle A\,=\,2.5dt

By simple trigonometry Failed to parse (Missing texvc executable; please see math/README to configure.): \scriptstyle d\,=\,2t(\cos{54^\circ}\,+\,\cos{18^\circ}) .

The side of a regular decagon inscribed in a unit circle is Failed to parse (Missing texvc executable; please see math/README to configure.): \tfrac{-1+\sqrt{5}}{2}=\tfrac{1}{\phi} , where ϕ is the golden ratio, Failed to parse (Missing texvc executable; please see math/README to configure.): \tfrac{1+\sqrt{5}}{2} .

A regular decagon is constructible using compass and straightedge:

An alternative (but similar) method is as follows:

There is one regular star polygon, the decagram {10/3}, using the same points, but connecting every third points. There are also two compounds: {10/4} is reduced to 2{5/2} as two pentagrams, and {10/2} is reduced to 2{5} as two pentagons.