One of the most important mathematical problems through all times has been to find the area of a polygon. for example, real estate areas often had the shape of polygons, and the tax was proportional to the area. suppose we have some polygon with vertices ("corners") specified by the coordinates (x1,y1), (x2,y2), (xn, yn), numbered either in a clockwise or anticlockwise fashion around the polygon. the area a of the polygon can amazingly be computed by just knowing the boundary coordinates: