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
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