Polygon Area

LINK:http://mathworld.wolfram.com/PolygonArea.html
Polygon Area
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PolygonArea

The (signed) area of a planar non-self-intersecting polygon with vertices (x_1,y_1), ..., (x_n,y_n) is

 A=1/2(|x_1 x_2; y_1 y_2|+|x_2 x_3; y_2 y_3|+...+|x_n x_1; y_n y_1|),

where |M| denotes a determinant. This can be written

 A=1/2(x_1y_2-x_2y_1+x_2y_3-x_3y_2+...+x_(n-1)y_n-x_ny_(n-1)+x_ny_1-x_1y_n),

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).

SEE ALSO: Area, Convex Polygon, Polygon, Triangle Area

REFERENCES:

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

posted on 2009-03-09 09:14 zmj 阅读(657) 评论(0)  编辑 收藏 引用


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