Pentagon

Pronunciation: /ˈpɛntəˌgɒn/ Explain

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

Click on the blue points and drag them to change the figure. Why are only two points shown in the figure? Manipulative 2 - Regular Pentagon Created with GeoGebra.

Properties of a Regular Pengagon

Click on the blue points and drag them to change the figure. Click on the check boxes to see the various properties of a pentagon. Manipulative 3 - Properties of a Pentagon Created with GeoGebra.

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 tilings in pentagonal patterns and tilings 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 . 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.

Tilings of Pentagons

• Figure 1: Tiling of a pentagon. Courtesy John Savard.

• Figure 2: Tiling of a pentagon.

Geometric nets that include pentagons

Example	Name	Printable Net
	Dodecahedron	net_dodecahedron.pdf
	Icosidodecahedron	net_icosidodecahedron.pdf
	Pentagonal Antiprism	net_pentagonal_antiprism.pdf
	Pentagonal Prism	net_pentagonal_prism.pdf
	Pentagonal Pyramid	net_pentagonal_pyramid.pdf
	Rhombidodecahedron	net_rhombidodecahedron.pdf
	Rombicosidodecahedron	net_rombicosidodecahedron.pdf
	Snub Dodecahedron	net_snub_dodecahedron.pdf
	Truncated Icosidodecahedron	net_trunc_icosidodecahedron.pdf
	Truncated Cuboctahedron	net_truncated_cuboctahedron.pdf
	Truncated Icosahedron	net_truncated_icosahedron.pdf
	Truncated Octahedron	net_truncated_octahedron.pdf
	Truncated Tetrahedron	net_truncated_tetrahedron.pdf

References

1. McAdams, David E.. All Math Words Dictionary, pentagon. 2nd Classroom edition 20150108-4799968. pg 136. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Stöcker, K.H.. The Elements of Constructive Geometry, Inductively Presented. pg 27. Translated by Noetling, William A.M, C.E.. www.archive.org. Silver, Burdett & Company. 1897. Last Accessed 12/3/2018. http://www.archive.org/stream/elementsofconstr00noetrich#page/27/mode/1up. Buy the book
3. Casey, John, LL.D., F.R.S.. The First Six Books of the Elements of Euclid. pg 9. Translated by Casey, John, LL.D. F.R.S.. www.archive.org. Hodges, Figgis & Co.. 1890. Last Accessed 12/3/2018. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/9/mode/1up/search/pentagon. Buy the book
4. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry. pg 9. www.archive.org. D. Van Nostrand Company. 1908. Last Accessed 12/3/2018. http://www.archive.org/stream/firstsixbooksofe00caseuoft#page/9/mode/1up/search/pentagon. Buy the book

More Information

• Wolchover, Natalie. Pentagon Tiling Proof Solves Century-Old Math Problem. https://www.quantamagazine.org. Quanta Magazine. 12/3/2018. https://www.quantamagazine.org/pentagon-tiling-proof-solves-century-old-math-problem-20170711/.

Cite this article as:

McAdams, David E. Pentagon. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/p/pentagon.html.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
12/1/2018: Removed broken links, updated license, implemented new markup, updated geogebra app. (McAdams, David E.)
8/28/2018: Corrected spelling. (McAdams, David E.)
8/7/2018: Changed vocabulary links to WORDLINK format. (McAdams, David E.)
12/31/2009: Initial version. (McAdams, David E.)