Decagon

Pronunciation: /ˈdɛk əˌgɒn/ Explain

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Manipulative 1 - Regular Decagon Created with GeoGebra.

A decagon is a ten sided polygon.[1] 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
FormulaDescription
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.

ImageDescription
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.

References

  1. Venugopal, Valsaraj. Higher Elementary Geometry. www.archive.org. 1st edition. pg 5. Last Accessed 8/6/2018. http://www.archive.org/stream/higherelementary033043mbp#page/n20/mode/1up/search/decagon. Buy the book
  2. Hornbrook, A. R.. Concrete geometry for beginners. pg 127. www.archive.org. American Book Company. 1895. Last Accessed 8/6/2018. http://www.archive.org/stream/concretegeometry00hornrich#page/127/mode/1up/search/decagon. Buy the book

More Information

  • McAdams, David E.. Geometric Nets. lifeisastoryproblem.com. Life is a Story Problem LLC. 3/12/2009. http://www.lifeisastoryproblem.com/explore/index_net.html.

Cite this article as:

McAdams, David E. Decagon. 7/3/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/decagon.html.

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Revision History

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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