Decagon

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Regular decagon

Edges and vertices	10
Schläfli symbols	{10} t{5}
Coxeter–Dynkin diagrams
Symmetry group	Dihedral (D₁₀)
Area (with t=edge length)	$A = \frac{5}{2}t^2 \cot \frac{\pi}{10}$ $= \frac{5t^2}{2} \sqrt{5+2\sqrt{5}}$ $\simeq 7.694208843 t^2.$
Internal angle (degrees)	144°

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 all internal angles equal to 4π/5 (144°). Its Schläfli symbol is {10}. The area of a regular decagon of side length a is given by

$\begin{align} A & = \frac{5}{2}a^2 \cot \frac{\pi}{10} = \frac{5a^2}{2} \sqrt{5+2\sqrt{5}} \\ & \simeq 7.694208843\, a^2. \end{align}$

[edit] Construction

A regular decagon is constructible with a compass and straightedge.

Complete steps 1 through 6 of constructing a pentagon.
Extend a line from each corner of the pentagon through the center of the circle made in step 1 of constructing a pentagon to the opposite side of that same circle.
The five corners of the pentagon constitute every other corner of the decagon. The remaining five corners of the decagon are those points where the lines of step 2 cross the original circle (but not a pentagon corner).

In short, a decagon is a ten sided shape.