If I know all the vertices of a particular polygon/figure, is there a generalized method/formula to calculate the area?
marked as duplicate by Rahul Narain, Ｊ. Ｍ., Gerry Myerson, Zev Chonoles Feb 7 '12 at 2:21
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If you know the two-dimensional cartesian coordinates of the vertices of a (non-self-intersecting, but can be non-convex) polygon, the Shoelace method will find its area. (Let me know if that article is not sufficiently clear and I'll try to explain it in more detail).