From: Michel.Bertler@deltacom.cam.org (Michel Bertler) Date: 20 Jan 95 20:17:00 Newsgroups: sci.math Subject: Area of a Pentagon ED>how do you find the area of a pentagon? You must first find the half angle value between each side of the regular figure, in this case the pentagon has five angles (10 half angles) of the same value given by: a = 90 - 180/n a = 90 - 180/5, 54 deg. where `a' is half angle value (degrees) `n' is number of angles or sides in the figure And from the above, find the `f' factor to multiply the squared value of a single side to get the figure total area: n x sin a x cos a 5 x sin 54 x cos 54 f = -----------------, f = -------------------, f = 1.720477 2 2 (2 cos a) (2 cos 54) Now, say we have a pentagon with one side 3 meters long, the pentagon total area would be: 2 A = fs , A = 1.720477 x 9, A = 15.4843 squared meters The above formulas work with all regular polygons. By regular meant same length in sides and angle values. Michel -- |GatorNet: Michel Bertler 128:200/0 |Internet: Michel.Bertler@deltacom.cam.org |