Where's the origin?
If the origin is inside the Minkowski difference, then the sum of all the areas of triangle formed by two consecutive vertices and the origin, is equal to the area of the Minkowski difference.
If the origin is outside, the sum of all the areas of triangle formed by two consecutive vertices and the origin, is always bigger than the area of the Minkowski difference. The area of the Minkowski difference in this case, is the difference between trigangles that overlap the Minkowski difference and triangles that are totally outside the Minkowski difference.
Calculating areas given vertices should be easy. Shoelace or whatever.
Good night.
