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 fivesided
polygon.
A regular pentagon is a fivesided
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
References
 McAdams, David E.. All Math Words Dictionary, pentagon. 2nd Classroom edition 201501084799968. pg 136. Life is a Story Problem LLC. January 8, 2015. Buy the book
 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
 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
 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
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
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.)