Difference between revisions of "Apothem"

Revision as of 20:58, 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, $n$ , and side length, $s$ , the length of the apothem is $\frac{s}{2\tan\left(\frac{\pi}{n}\right)}$ .

Given the number of sides, $n$ , and radius of the circumscribed circle, $R$ , the length of the apothem is $R\cos\left(\frac{\pi}{n}\right)$ .

Given the length of the apothem, $a$ , and the perimeter, $p$ , of the polygon, the area of the polygon is $\frac{ap}{2}$ or $as$ , where $s$ is the semiperimeter.

@@ Line 9: / Line 9: @@
 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 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]].
+Given the length of the apothem, <math>a</math>, 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]]

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Difference between revisions of "Apothem"

Revision as of 20:58, 1 November 2006

Formulas