Pronunciation: /ˈɒk.təˌgɒn/ Explain

Click on the blue points and drag them to change the figure.

Manipulative 1 - Octagon Created with GeoGebra.

Click on the blue points and drag them to change the figure.

Manipulative 2 - Regular Octagon Created with GeoGebra.

A octagon is any eight sided polygon. A regular octagon is an eight-sided polygon with sides of equal length.

As long as the sides do not intersect, the figure in manipulative 1 is an octagon.

Octagon Facts
Central Anglebeta=45 degrees or p/4 radians.
Vertex Anglealpha=135 degrees or (3pi)/4 radians.
Exterior Anglegamma=225 degrees or (5pi)/4 radians
Inradiusr=(1/2)*(1+square root(2))
Circumradius(1/2)*square root(4+2*square root(2)
Arear=2*(1+square root(2))s^2
Table 1

Geometric Nets Using Octagons
Octagonal Prism
Octagonal Antiprism
Table 2

Examples of Octagons

Stop signBlue gemstone (lapis lazuli) with gold trim, irregular octagon shaped.


  1. McAdams, David E.. All Math Words Dictionary, octagon. 2nd Classroom edition 20150108-4799968. pg 129. Life is a Story Problem LLC. January 8, 2015. Buy the book

Cite this article as:

McAdams, David E. Octagon. 3/25/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/o/octagon.html.

Image Credits

Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
9/5/2018: Removed broken links, updated license, implemented new Geogebra protocol, implemented new markup. (McAdams, David E.)
12/21/2009: Added "References". (McAdams, David E.)
12/30/2008: Changed equations to images. (McAdams, David E.)
7/1/2008: Initial version. (McAdams, David E.)

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