Polygon Area
The (signed) area of a planar non-self-intersecting polygon with vertices 
, ...,
is
 |
where 
denotes a determinant.
This can be written
 |
where the signs can be found from the diagram above.
Note that the area of a convex polygon is defined to be positive if the points are arranged in a counterclockwise order, and negative if they are in clockwise order (Beyer 1987).
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polygon area
