Difference between revisions of "Apothem"
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| − | The apothem of a [[regular | + | The '''apothem''' of a [[regular polygon]] is the [[line segment]] drawn from the [[center]] of the [[polygon]] [[perpendicular]] to one of its [[edge]]s. It is also the [[radius]] of the [[incircle | inscribed circle]] of the polygon. |
== Formulas == | == Formulas == | ||
| − | Given the | + | Given the number of sides, <math>n</math>, and side length, <math>s</math>, the length of the apothem is <math>\frac{s}{2\tan\left(\frac{\pi}{n}\right)}</math>. |
| − | Given the | + | Given the number of sides, <math>n</math>, and radius of the [[circumcircle | circumscribed circle]], <math>R</math>, the length of the apothem is <math>R\cos\left(\frac{\pi}{n}\right)</math>. |
| − | Given the | + | Given the length <math>a</math> of the apothem and the [[perimeter]] <math>p</math> of the polygon, the [[area]] of the polygon is <math>\frac{ap}{2}</math> or <math>as</math>, where <math>s</math> is the [[semiperimeter]]. |
[[Category:Definition]] | [[Category:Definition]] | ||
Revision as of 13:16, 1 November 2006
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The apothem of a regular polygon is the line segment drawn from the center of the polygon perpendicular to one of its edges. It is also the radius of the inscribed circle of the polygon.
Formulas
Given the number of sides, 
, and side length, 
, the length of the apothem is 
.
Given the number of sides, , and radius of the circumscribed circle, 
, the length of the apothem is 
.
Given the length 
of the apothem and the perimeter 
of the polygon, the area of the polygon is 
or 
, where is the semiperimeter.
