Surveyor's Formula

Date: 06/05/99 at 11:20:14
From: Alessandro Pagani
Subject: Area of irregular nonconvex polygon

I'm a student of the Politecnico di Milano (Italy) as an environmental 
engineer. I need a method to calculate the area of an irregular 
polygon in a Visual Basic program. On your website, I've read about a 
formula to be used in a program when I have the lengths of all the 
sides and some of the angles.

My problem is different: I have all the spatial topographic 
coordinates of the points of a drainage area that may be nonconvex.

Can you help me? Thanks.

Date: 06/06/99 at 08:25:42
From: Doctor Jerry
Subject: Re: Area of irregular nonconvex polygon

Hello Alessandro,

You can use the "surveyor's formula." It gives the area of any planar 
polygon. If the vertices are (x1,y1), (x2,y2), ..., (xn,yy), then

A = (1/2)[Det(x1,x2,y1,y2)+Det(x2,x3,y2,y3)+ ... +Det(xn,x1,yn,y1)],

   where Det(a,b,c,d) = a*d-b*c.

- Doctor Jerry, The Math Forum
  http://mathforum.org/dr.math/