Associated Topics || Dr. Math Home || Search Dr. Math

### 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
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/
```
Associated Topics:
High School Geometry
High School Practical Geometry
High School Triangles and Other Polygons

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search