The length of the radius of the inscribed circle of a regular n-gon is called the apothem of the n-gon. Prove that the area, A, of a regular n-gon can be computed using the following formula: A = aP/2 , where a represents the apothem and P the perimeter of the regular n-gon.

The length of the radius of the inscribed circle of a regular n-gon is called the apothem of the n-gon. Prove that the area, A, of a regular n-gon can be computed using the following formula: A = aP/2 , where a represents the apothem and P the perimeter of the regular n-gon.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter8: Areas Of Polygons And Circles

Section8.3: Regular Polygons And Area

Problem 12E: If the area (A=12aP) and the perimeter of a regular polygon are numerically equal, find the length...

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