Pronunciation: /ˈdɛk.əˌgɒn/ Explain

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Manipulative 1 - Regular Decagon Created with GeoGebra.

A decagon is a ten sided polygon.[2] A regular decagon is a ten sided regular polygon. In table 1, a is the length of a side and n is the number of sides.

Formula for regular decagon
n=10Number of sides
gamma=360/n=36 degreesCentral angle
A=(1/2)n*a^2*cot(pi/n) about 7.69*a^2Area
alpha=(2*(n-2)*90)/n=144Interior angle
beta=(180*(n+2))/n=216Exterior angle
r=(1/2)*a*cos(pi/n) about 0.48aInradius
r=(1/2)*a*csc(pi/n) about 1.62aCircumradius
Table 1

Geometric Nets

A geometric net is a 2-dimensional shape that folds into a 3-dimensional polyhedron. Some geometric nets that contain at least 1 decagon are shown in table 2.

Net of an decagonal frustum.Net of a decagonal frustum.
Net of an decagonal antiprism.Net of a decagonal antiprism.
Net of an decagonal prism.Net of a decagonal prism.
Net of an pentagonal cupola.Net of a pentagonal cupola.
Net of an pentagonal rotunda.Net of a pentagonal rotunda.
Net of an truncated dodecahedron.Net of a truncated dodecahedron.
Net of an truncated icosidodecahedron.Net of a truncated icosidodecahedron.
Table 2: Geometric nets that contain decagons.


  1. McAdams, David E.. All Math Words Dictionary, decagon. 2nd Classroom edition 20150108-4799968. pg 54. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. Venugopal, Valsaraj. Higher Elementary Geometry. 1st edition. pg 5. Last Accessed 7/3/2018. Buy the book
  3. Hornbrook, A. R.. Concrete geometry for beginners. pg 127. American Book Company. 1895. Last Accessed 7/3/2018. Buy the book

More Information

  • McAdams, David E.. Geometric Nets. Life is a Story Problem LLC. 3/12/2009.

Cite this article as:

McAdams, David E. Decagon. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
7/3/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
1/22/2010: Added "References". (McAdams, David E.)
1/21/2009: Added geometric nets containing decagons, Geometric Nets. (McAdams, David E.)
12/4/2008: Initial version. (McAdams, David E.)

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