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Nonagon

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Revision as of 15:15, 29 May 2024 by imported>Manjuew (Every interior angle of a regular nonagon is 140 degrees and they add up to 1260 degrees.)
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File:Enneagon.svg
A nonagon

A nonagon or 9-gon is a shape with 9 sides and 9 corners.

Regular nonagon[change]

All sides of a regular nonagon are the same length. Each corner is 140°. All corners added together equal 1260°.

Area[change]

The amount of space a regular nonagon takes up is

<math>A = \frac{9}{4}a^2\cot\frac{\pi}{9}=(9/2)ar = 9r^2\tan(\pi/9) </math>
<math>= (9/2)R^2\sin(2\pi/9)\simeq6.18182\,a^2.</math>

a is the length of one of its sides.

Tilings[change]

The regular enneagon can tessellate the euclidean tiling with gaps. These gaps can be filled with regular hexagons and isosceles triangles. In the notation of symmetrohedron this tiling is called H(*;3;*;[2]) with H representing *632 hexagonal symmetry in the plane.

File:Conway tiling dKH.png