If D is the mid point of side of side BC of a traingle ABC, P and Q are two points lying respectively on the sides AB and BC such that DP is parallel to QA. Prove that ar(triangle CQP) = 1/2 ar(traingle ABC).

Answer 1

You must have a typo.
Make ABC a 3-4-5 right triangle, and let AQ be the altitude to the hypotenuse.
The areas do not fit your hypothesis.

Answer 2

Thank you