# Difference between revisions of "Shoelace Theorem"

Line 9: | Line 9: | ||

<cmath>(a_1, b_1)</cmath> | <cmath>(a_1, b_1)</cmath> | ||

+ | |||

<cmath>(a_2, b_2)</cmath> | <cmath>(a_2, b_2)</cmath> | ||

+ | |||

<cmath>\vdots</cmath> | <cmath>\vdots</cmath> | ||

+ | |||

<cmath>(a_n, b_n)</cmath> | <cmath>(a_n, b_n)</cmath> | ||

+ | |||

<cmath>(a_1, b_1)</cmath> | <cmath>(a_1, b_1)</cmath> | ||

## Revision as of 12:07, 24 April 2008

**Shoelace Theorem** is a nifty formula for finding the area of a polygon given the coordinates of it's vertices.

## Theorem

Let the coordinates, in "clockwise" order, be , , ... , . The area of the polygon is

Shoelace Theorem gets it's name by listing the coordinates like so:

## Proof

*This article is a stub. Help us out by expanding it.*