Octagon
From Wikipedia, the free encyclopedia
- For other uses, see Octagon (disambiguation).
In geometry, an octagon is a polygon that has eight sides.
In some parts of the world, stop signs are in the shape of a regular octagon.
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[edit] Regular octagons
A regular octagon is an octagon whose sides are all the same length and whose internal angles are all the same size.
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
- <math>A = 2a^2 \cot \frac{\pi}{8} = 2(1+\sqrt{2})a^2 \simeq 4.82843 a^2.</math>
In terms of <math>R</math>, the area is <math>8R^2/(1+\sqrt{2})</math> <p>In terms of <math>r</math>, the area is <math>8r^2/(11+9\sqrt{2})</math>
[edit] Construction
An 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.
[edit] See also
[edit] External links
- How to find the area of an octagon
- Definition and properties of an octagon With interactive animation
| Polygons |
|---|
| Triangle | Quadrilateral | Pentagon | Hexagon | Heptagon | Octagon | Enneagon (Nonagon) | Decagon | Hendecagon | Dodecagon | Triskaidecagon | Pentadecagon | Hexadecagon | Heptadecagon | Enneadecagon | Icosagon | Icosihenagon | Tricontagon | Pentacontagon | Hectagon | Chiliagon | Myriagon |
es:Octógono fr:Octogone it:Ottagono he:תמניון ka:ოქტაგონი nl:Achthoek ja:八角形 pl:Ośmiokąt pt:Octógono fi:Kahdeksankulmio sv:Oktagon
th:รูปแปดเหลี่ยม
