The shoelace formula
The shoelace formula finds a simple polygon's signed area from ordered coordinates. It multiplies each x-coordinate by the next y-coordinate, subtracts the reverse products and halves the absolute total.
Coordinate order matters
Follow the polygon boundary clockwise or counterclockwise. Randomly ordered points can create crossed edges and a misleading result.
Polygon centroid
The centroid shown is the geometric centre of the polygon's area, not simply the average of its vertices.