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>, 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).