Apothem

Pronunciation: /ˈæpəˌθɛm/ ?

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Manipulative 1: Apothem and sagitta. Click on the blue points and drag to change the figure.

The apothem of a regular polygon is a line segment from the center of the polygon to the midpoint of one of its sides.[1] 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, the 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.

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Manipulative 2: Apothem 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 parallel with the apothem. In manipulative 2 the sagitta is labeled S. Together, the sagitta and the apothem makes a radius of the circle.

Cite this article as:


Apothem. 2010-10-23. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/apothem.html.

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Revision History


2010-10-23: Added text for sagitta of a regular polygon. (McAdams, David.)
2010-01-06: Added "References" (McAdams, David.)
2008-12-19: Clarified wording of a apothem of a chord of a circle. Added vocabulary link to 'chord' (McAdams, David.)
2008-04-18: Initial version (McAdams, David.)

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