From: kovarik@mcmail.cis.McMaster.CA (Zdislav V. Kovarik)
Subject: Re: Formula For Area Of A Polygon
Date: 21 Jan 1999 01:17:35 -0500
Newsgroups: sci.math
Keywords: Polygon areas with Green's theorem (and little cancellation)

In article <785o89$5k0$1@nnrp1.dejanews.com>,  <cls2jmg@ffic.com> wrote:
>Does anyone know the formula for the area of a polygon?
>I have the lengths for each of the seven sides that
>make up this polygon.  I would like to generate the
>area.  Do I need more information?

As others pointed out, you need more information; even with four sides,
you can change the angles around to make the area small or big, and with
seven sides, there is even more flexibility. Make a model from sticks.

If you have x-y coordinates of the vertices, there is help:

Definition:
           Area = integral[over the region] (1 dx dy)

Use Green's Formula (the user is responsible for the 
counterclockwise ordering of the vertices):

Suppose P_j = (x_j, y_j) , j=1,...,n are the vertices of F, and
define  P_(n+1) = P_1,

 u_j = x_(j+1) - x_j
 v_j = y_(j+1) - y_j

then

 Area = (1/2) * sum(x_j * v_j - y_j * u_j)

An algebraically equivalent but cruder formula which may lead to greater
loss of accuracy due to cancellation is

 Area = (1/2) * sum(x_j * y_(j+1) - x_(j+1) * y_j)

Good luck, ZVK(Slavek).