# Octagon

An octagon is a polygon that has eight sides. The internal angle at each vertex of a regular octagon is 135°. The area of a regular octagon of side length a is given by

[itex]A = 2a^2 \cot \frac{\pi}{8} = 2(1+\sqrt{2})a^2 \simeq 4.82843 a^2.[itex]
 Missing imageOctagon.jpgRegular Octagon Missing imageConcave_octagon.pngConcave Octagon Missing imageComplex_octagon.pngComplex Octagon regular irregular concave complex

Worldwide, stop signs are regular octagons.

## Octagon construction

A regular octagon is constructible with straightedge and compass. To do so, follow steps 1 through 18 of the animation, noting that the compass radius is not altered during steps 7 though 10.

Missing image
OctagonConstructionAni.gif
Octagon Construction Animation

## Octagons in general use

The most common use of Octagons are for the shape of stop signs.

In architecture, an octagon house is a house built in an octagonal shape. Monticello is the most famous example.

In mixed martial arts, The Octagon is the name of the octagonal ring used in the Ultimate Fighting Championship, and by metonymy a term for the UFC itself as well.

The Octagon is the name of the city centres of Bristol, England, and Dunedin, New Zealand.

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