# How to Prove these Areas are Equal?

This was a question from the British Mathematical Olympiad (Round 1 2007).

In the convex quadrilateral ABCD, points M,N lie on the side AB such that AM = MN =NB, and points P, Q lie on the side CD such that CP = PQ = QD. Prove that Area of AMCP = Area of MNPQ = 1/3 Area of ABCD.

I was stuck on it for some time… until I realised I had misread the question and was looking at the…