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
|