Known values: Cartesian coordinates of all vertices (x1, y1), (x2, y2), â€¦(xn, yn).
Solution: Area A of simple polygonal shape.
1. Subtract surrounding trapezoids (red) from encompassing trapezoids (green).
2. In general:
- A is the area of the polygon,
- n is the number of sides (or vertices) of the polygon,
- xi, yi, i=1, 2, â€¦, n are the Cartesian coordinates of polygonâ€™s vertices, and
- +1 or -1 define next or previous vertex from i vertex.
If vertices are numbered clockwise, the determinants of the expressions above are positive whereas if numbered counterclockwise, they are negative in which case absolute values should be considered.