area of regular polygon

Theorem 1.

Given a regularPlanetmathPlanetmathPlanetmathPlanetmath n-gon ( with apothem of length a and perimeterPlanetmathPlanetmath ( P, its area is


Given a regular n-gon R, line segmentsMathworldPlanetmath can be drawn from its center to each of its vertices. This divides R into n congruent trianglesMathworldPlanetmath. The area of each of these triangles is 12as, where s is the length of one of the sides of the triangle. Also note that the perimeter of R is P=ns. Thus, the area A of R is


To illustrate what is going on in the proof, a regular hexagon appears below with each line segment from its center to one of its vertices drawn in red and one of its apothems drawn in blue.

Title area of regular polygon
Canonical name AreaOfRegularPolygon
Date of creation 2013-03-22 17:11:06
Last modified on 2013-03-22 17:11:06
Owner Wkbj79 (1863)
Last modified by Wkbj79 (1863)
Numerical id 6
Author Wkbj79 (1863)
Entry type Theorem
Classification msc 51-00