A Parallelogram and a Triangle between the Same Parallels
P and Q are a...
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)