# Difference between revisions of "Shoelace Theorem"

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− | The '''Shoelace Theorem''' is a nifty formula for finding the [[area]] of a [[polygon]] given the [[Cartesian coordinate system | coordinates]] of | + | The '''Shoelace Theorem''' is a nifty formula for finding the [[area]] of a [[polygon]] given the [[Cartesian coordinate system | coordinates]] of its [[vertex|vertices]]. |

==Theorem== | ==Theorem== |

## Revision as of 21:26, 3 August 2008

The **Shoelace Theorem** is a nifty formula for finding the area of a polygon given the coordinates of its vertices.

## Theorem

Suppose the polygon has vertices , , ... , , listed in clockwise order. Then area of is

The Shoelace Theorem gets its name because if one lists the the coordinates in a column, and marks the pairs of coordinates to be multiplied, the resulting image looks like laced-up shoes.

## Proof

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