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
A regular pentagon is a five-sided
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
- 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
- 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
- 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
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.
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.)