For showing area of AMCP = 1/3 area of ABCD, draw the diagonal AC and see where it gets you. For this one, you don't need the lines MQ, NP, and indeed, they might be distracting, so try to just draw the lines you've got and see if you can spot something.
For the MNPQ one, you could try something similar. (Basically, with these kind of questions, usually just draw lots of diagonals making everything into smaller triangles and the solution will pop up eventually.)
I'm not sure if I've got the best solution, but a hint is that it might be easier showing area of MNPQ = area of AMCP, rather than MNPQ = 1/3 area of ABCD. Experiment a little and see what you get.