In triangles POA and QOC, we have
∠AOP = ∠COQ [vertically opposite angles]
OA = OC [Diagonals of a parallelogram bisect each other]
∠PAC = ∠QCA [ AB || DC; alternative angles]
So, by ASA congruence criterion, we have
ΔPOA ≅ QOC
Area ( ΔPOA) = area (ΔQOC)