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).

Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 123-124, 1987.

CITE THIS AS:

Weisstein, Eric W. "Polygon Area." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/PolygonArea.html