Concave Polygon

Pronunciation: /ˈkɒn keɪv ˈpɒ liˌgɒn/ ?
concave polygon
Figure 1: Concave Polygon

Figure 1 is an example of a concave polygon. Note that part of the line between the two points in the figure lie outside the polygon.

convex polygon
Figure 2: Convex polygon

Figure 2 is an example of a convex polygon. Note that the entire line is contained within the polygon. In fact, a line drawn between any two points that are part of the polygon will be entirely contained within the polygon.

A polygon is a closed shape whose boundaries consist of straight lines. A polygon is concave if, for any two points that are part of the shape, a straight line can be drawn between the two points that lies outside the shape.[1] A property of concave polygons is that if the sides are extended, the extension of at least two sides will intersect one of the other sides.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)
Manipulative 1: Concave and convex polygons. Click on the blue points and drag them to change the figure. Created with GeoGebra


  1. concave polygon. Encyclopedia Britannica. (Accessed: 2010-01-05). polygon.
  2. Beman, Wooster Woodruff; and Smith, David Eugene. New Plane and Solid Geometry, pg 54. Ginn & Company, 1899. (Accessed: 2010-01-18).
  3. Lyman, Elmer A.. Plane and Solid Geometry, pg 57. American Book Company, 1908. (Accessed: 2010-01-18).

Cite this article as:

Concave Polygon. 2010-01-18. All Math Words Encyclopedia. Life is a Story Problem LLC.


Image Credits

Revision History

2010-01-19: Corrected description of figure 1, added manipulative 1 (McAdams, David.)
2010-01-18: Added "References" (McAdams, David.)
2007-07-30: Initial version (McAdams, David.)

All Math Words Encyclopedia is a service of Life is a Story Problem LLC.
Copyright © 2005-2011 Life is a Story Problem LLC. All rights reserved.
Creative Commons License This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License