This is another simple problem from *Five Hundred Mathematical Challenges*:

**“Problem 57.** Let *X* be any point between *B* and *C* on the side *BC* of the convex quadrilateral *ABCD *(as in the Figure). A line is drawn through *B *parallel to *AX *and another line is drawn through *C *parallel to *DX*. These two lines intersect at *P*. Prove that the area of the triangle *APD *is equal to the area of the quadrilateral *ABCD*.”

See the Triangle Quadrangle Puzzle