Originally Posted by

**xwrathbringerx** **Question**

In a quadrilateral ABCD, P and R are the midpoints of AB and CD respectively. Also Q and S are points on the sides BC and DA respectively such that BQ = 2QC and DS = 2SA. Prove that the area of the quadrilateral PQRS equals S/2 where S is the area of the quadrilateral ABCD.

**Solution**

**Line P R divide quadrilateral ABCD with equal area s/2:**

A (APRD) = A (PBCR) = S / 2

Sum of the triangle area PRS and PQR is area of the quadrilateral PQRS and is s/2.

It is s/2 not only for BQ = 2QC and DS = 2SA, it is true for

BQ = N*QC and DS = N*SA

where N=(1/M or M) and M real number.

Triangle area PRS(1/M) equal PQR(M), sum=S/2 and

PQR(1/M) equal PRS(M), sum=S/2

**I was wondering if this is how you do the question? **