Pentagon

Pronunciation: /ˈpɛntəˌgɒn/ ?

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Manipulative 1: Pentagon. Created with GeoGebra.

A pentagon is a five-sided polygon. A regular pentagon is a five-sided equilateral polygon. Click on the blue points in manipulatives 1 and 2 and drag them to change the figure.

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Manipulative 2: Properties of a regular pentagon. Created with GeoGebra.

Properties of a Pengagon

  • A pentagon has five sides.
  • The center of a pentagon can be found at the intersection of the perpendicular bisectors of any two sides.
  • There are many tesselations in pentagonal patterns and tesselations that use pentagons. See below.
  • The central angle of a pentagon measures 72° or 2π/5 radians. The central angle is the angle between two line segments from the center of the pentagon to two adjacent vertices. See manipulative 2.
  • The internal angle of a pentagon measures 108° or 3π/5 radians. The internal angle is the angle between two sides on the inside of the pentagon.
  • The area of a regular pentagon in terms of one of it sides is A=t^2*square root(25+10*square root(5))/4..
  • The apothem of a regular pentagon is a line segment from the midpoint of one side of the pentagon to the pentagon's center.
  • There are many geometric nets that include pentagons. See below.

Tesselations of Pentagons

  • A complicated tesselation of a pentagon
    Figure 1: Tesselation of a pentagon. Courtesy John Savard. Click on the image to see a full size version.
  • A complicated tesselation of a pentagon
    Figure 2: Tesselation of a pentagon.

Geometric nets that include pentagons

ExampleNamePrintable Net
Dodecahedronnet_dodecahedron.pdf
Icosidodecahedronnet_icosidodecahedron.pdf
Pentagonal Antiprismnet_pentagonal_antiprism.pdf
Pentagonal Prismnet_pentagonal_prism.pdf
Pentagonal Pyramidnet_pentagonal_pyramid.pdf
Rhombidodecahedronnet_rhombidodecahedron.pdf
Rombicosidodecahedronnet_rombicosidodecahedron.pdf
Snub Dodecahedronnet_snub_dodecahedron.pdf
Truncated Icosidodecahedronnet_trunc_icosidodecahedron.pdf
Truncated Cuboctahedronnet_truncated_cuboctahedron.pdf
Truncated Icosahedronnet_truncated_icosahedron.pdf
Truncated Octahedronnet_truncated_octahedron.pdf
Truncated Tetrahedronnet_truncated_tetrahedron.pdf

References

  1. Stöcker, K.H.. The Elements of Constructive Geometry, Inductively Presented, pg 27. Translated by Noetling, William A.M, C.E.. Silver, Burdett & Company, 1897. (Accessed: 2009-12-31). http://www.archive.org/stream/elementsofconstr00noetrich#page/27/mode/1up.
  2. Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid, pg 9. Casey, John, LL.D. F.R.S.. Hodges, Figgis & Co., 1890. (Accessed: 2010-01-02). http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/9/mode/1up/search/pentagon.
  3. pentagon. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=pentagon&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  4. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry, pg 9. D. Van Nostrand Company, 1908. (Accessed: 2010-01-02). http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/9/mode/1up/search/pentagon.

More Information

Cite this article as:


Pentagon. 2009-12-31. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/p/pentagon.html.

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2009-12-31: Initial version (McAdams, David.)

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