The following java method calculates the sum of a polygon given a list of the points in either clockwise or counter clockwise order:

private double calculateArea(List<Point> orderedPoints) { //multiply each x coordinate by the following y int positiveDiagonalSum = 0; for (int i = 0; i<orderedPoints.size(); i++){ if (i == orderedPoints.size() - 1){ positiveDiagonalSum += orderedPoints.get(i).x * orderedPoints.get(0).y; } else { positiveDiagonalSum += orderedPoints.get(i).x * orderedPoints.get(i+1).y; } } //multiply each y coordinate by the following x int negativeDiaglonalSum = 0; for (int i = 0; i<orderedPoints.size(); i++){ if (i == orderedPoints.size() - 1){ negativeDiaglonalSum += orderedPoints.get(i).y * orderedPoints.get(0).x; } else { negativeDiaglonalSum += orderedPoints.get(i).y * orderedPoints.get(i+1).x; } } //subtract second sum from first, divide by 2 double area = Math.abs((positiveDiagonalSum - negativeDiaglonalSum) / 2.0); return area; }