[This problem is worth 7 points.]
Convex quadrilateral ABCD has an area of 10. Side AB has a length of 6, BC of 7, CD of 8, and DA of 9. Each side of the quadrilateral is then extended beyond one of its endpoints, with AB extended beyond B to a new point B', BC extended beyond C to a new point C', and so on. Each of the extended sides is twice the length of the original side (so AB' is of length 12). Find the area of the quadrilateral A'B'C'D'.
