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Question

Question 3
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).

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Solution


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)=12Area(ABCD)...(1)
Similarly, ΔAPB and parallelogram ABCD lie on the same base AB and between the same parallel lines AB and DC.
Area(ΔAPB)=12Area(ABCD)...(2)
From equation (1) and (2), we obtain;
Area(ΔBQC)=Area(ΔAPB)


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