Decagon

Pronunciation: /ˈdɛk əˌgɒn/ ?

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Manipulative 1: Regular dodecagon. Created with GeoGebra.

A decagon is a ten sided polygon.[1] A regular decagon is a ten sided regular polygon. Click on the blue points in manipulative 1 and drag them to change the figure. 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. Click on the image of the net to load a full page net that can be printed.

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. decagon. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=decagon&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Venugopal, Valsaraj. Higher Elementary Geometry, 1st edition, pg 5. (Accessed: 2010-01-22). http://www.archive.org/stream/higherelementary033043mbp#page/n20/mode/1up/search/decagon.
  3. Hornbrook, A. R.. Concrete geometry for beginners, pg 127. American Book Company, 1895. (Accessed: 2010-01-22). http://www.archive.org/stream/concretegeometry00hornrich#page/127/mode/1up/search/decagon.

More Information

  • McAdams, David. Geometric Nets. lifeisastoryproblem.com. Life is a Story Problem LLC. 2009-03-12. http://www.lifeisastoryproblem.com/explore/index_net.html.

Cite this article as:


Decagon. 2010-01-22. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/d/decagon.html.

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Revision History


2010-01-22: Added "References" (McAdams, David.)
2009-01-21: Added geometric nets containing decagons, Geometric Nets (McAdams, David.)
2008-12-04: Initial version (McAdams, David.)

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