In figure, ABCD and AEFD are two parallelograms. Prove that `ar (Delta – InterviewSolution

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1.	In figure, ABCD and AEFD are two parallelograms. Prove that `ar (DeltaPEA) = ar (DeltaQFD)`.
Answer» Given, ABCD and AEFD are two parallelograms. To prove `" " ar(DeltaPEA) = ar (DeltaQFD)` Proof In quadrilateral PQDA, `AP\|\| DQ" "` [since, in parallelogram ABCD, `AB \|\|CD`] and `" " PQ \|\| AD" "` [since, in parallelogram AEFD, `FE \|\| AD`] Then, quadrilateral PQDA is a parallelogram. Also, parallelogram PQDA and AEFD are on the same base AD and between the same parallels AD and EQ. `therefore" "` ar (parallelogram PQDA) = ar (parallelogram AEFD) On subtracting ar (quadrilateral APFD) from both sides, we get ar (parallelogram PQDA)- ar (quadrilateral APFD) = ar (parallelogram AEFD) - ar (quadrilateral APFD) `rArr" "` `ar (DeltaQFD) = ar (DeltaPEA)" "` Hence proved.

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