Apothem

Pronunciation: /ˈæpəˌθɛm/ Explain
Click on the blue points and drag them to change the figure.

How many apothems does a pentagon have?
Manipulative 1 - Apothem and Sagitta Created with GeoGebra.

An apothem of a regular polygon is a line segment from the center of the polygon to the midpoint of one of its sides. An apothem is always perpendicular to the side that contains the midpoint. Since the midpoint of each side of a regular polygon is intersected by the incircle, an apothem is a radius of the incircle. The sagitta is the line segment from the edge of the regular polygon to the edge of the circumcircle of the regular polygon that is collinear with the apothem.

Click on the blue points in manipulative 1 and 2 and drag them to change the figure.

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

Manipulative 2 - Apothem and Sagitta of a Circle Created with GeoGebra.

The apothem of a chord of a circle is a line segment from the center of the circle to the midpoint of a chord of the circle. In manipulative 2, the apothem is labeled r. The sagitta is the line segment from the midpoint of the chord to the edge of the circle that is collinear with the apothem. In manipulative 2 the sagitta is labeled S. Together, the sagitta and the apothem make a radius of the circle.

Cite this article as:

McAdams, David E. Apothem. 6/14/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/apothem.html.

Image Credits

Revision History

6/14/2018: Removed broken links, changed Geogebra links to work with Geogebra 5, updated license, implemented new markup. (McAdams, David E.)
10/23/2010: Added text for sagitta of a regular polygon. (McAdams, David E.)
1/6/2010: Added "References". (McAdams, David E.)
12/19/2008: Clarified wording of a apothem of a chord of a circle. Added vocabulary link to 'chord' (McAdams, David E.)
4/18/2008: Initial version. (McAdams, David E.)

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