P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB) = ar (BQC)

It can be observed that ΔBQC and parallelogram ABCD lie on the same base BC and these are between the same parallel lines AD and BC

Area (ΔBQC) = Area (ABCD) (i)

Similarly,

ΔAPB and parallelogram ABCD lie on the same base AB and between the same parallel lines AB and DC

Area (ΔAPB) = Area (ABCD) (ii)

From equation (i) and (ii), we get

Area (ΔBQC) = Area (ΔAPB)