Difference between revisions of "Shoelace Theorem"
m |
m (it's-->its) |
||
| Line 1: | Line 1: | ||
| − | 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 20:26, 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
![\[\dfrac{1}{2} |a_1b_2+a_2b_3+\cdots +a_nb_1-b_1a_2-b_2a_3-\cdots -b_na_1|.\]](http://latex.artofproblemsolving.com/0/0/f/00fb3ab55fb21e342cd434b951e5acea267f35cc.png)
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.
