Calculate area of a figure based on vertices 
Possible Duplicate:
How quickly we forget - basic trig. Calculate the area of a polygon
How to calculate the area of a polygon? 

If I know all the vertices of a particular polygon/figure, is there a generalized method/formula to calculate the area?

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).
