(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let C be the line segment connecting the points (x_{1},y_{1}) and (x_{2},y_{2}). More over let the line integral over C of (x dy - y dx) = x_{1}y_{2}- x_{2}y_{1}.

Suppose the vertices of a polygon, listed in counter-clockwise order, are (x_{1}y_{1}), (x_{2}y_{2}), ... , (x_{n}y_{n}). Show that the area of the polygon is

(1/2) * ((x_{1}y_{2}- x_{2}y_{1}) + (x_{2}y_{3}- x_{3}y_{2}) + ... + (x_{n}y_{1}- x_{1}y_{n}))

2. Relevant equations

I don't know a relevant equation, but I suspect there probably is one.

3. The attempt at a solution

So, basically, I just want to say something like, let C* be the set of all line segments that connect, with positive orientation, (x_{1}y_{1}), (x_{2}y_{2}), ... , (x_{n}y_{n}). Then using the fact that the line integral over C of (x dy - y dx) = x_{1}y_{2}- x_{2}y_{1}, and by repeatedly applying this fact, I would have something like:

[itex]\sum[/itex]_{* = 1}^{n}of ([itex]\int[/itex]_{C*}(x dy - y dx)). I think this gives the desired result except for the 1/2, which still eludes me.

Also, how do you format these sigmas? It's supposed to read "Sigma from *=1 to n"

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Summing n-number of Terms to Find the Area of a Polygon

**Physics Forums | Science Articles, Homework Help, Discussion**