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In Geometry , an octagon is a Polygon that has Eight sides.


REGULAR OCTAGONS

A Regular Octagon is an octagon with equal 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
:A = 2a^2 \cot rac{\pi}{8} = 2(1+\sqrt{2})a^2 \simeq 4.82843 a^2.

In terms of R, the area is 8R^2/(1+sqrt{2})

In terms of r, the area is 8r^2/(11+9sqrt{2})
s are regular octagons]]


Construction

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


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. Examples include Thomas Jefferson 's '' Poplar Forest ,'' near Lynchburg , Virginia and the Tayloe House (now simply called the "Octagon House") in Washington, D.C. , designed by William Thornton for Colonel John Tayloe .

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 .

Oktogon is a major square in downtown Budapest , the crossing point of Andrássy Avenue and the Grand Boulevard . tee hee


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