Question

p and q are any two points lying on the sides dc and ad respectively of parellelogram abcd show that ar (apb)=ar(bqc)

Answer 1

ar(APB) = 1/2ar(ABCD) [they both lies on the same base AB and between the same parallels AB||CD]
and ar(BQC)=1/2ar(ABCD) [ they lies on the same base BC and between same parallels BC||AD]

since both of their areas are equal to 1/2ar(ABCD)
therefore , ar(APB)= ar(BQC)