# PQRS is a parallelogram with diagonals PR and QS intersecting at a point E.If ar(ΔSEP) + ar(ΔQER)=12cm²,find area of parallelogram PQRS.

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by KSA

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by KSA

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Given: In thr figure, PQRS is a parallelogram, Diagonal PR and QS meets at point E. ar(ΔSEP)+ar(ΔQER)=12cm²

To find: area of parallelogram PQRS

Construction: Draw perpedicular AB passing through E

Solution: In parallelogram PQRS

SP=QR and SPIIQR ..(1)

ar(ΔSEP)+ar(ΔQER)=12cm²

1/2×PS×AE+1/2×BE×QR=12cm² (area of Δ=base×height, AE is now height of ΔSEP and BE of ΔQER)

1/2×QR×AE+1/2×BE×QR=12cm² (from (1) )

1/2QR(AE+BE)=12cm²

QR×AB=24cm²

QR and AB are the base and height of IIgm PQRS

Therefore, area of IIgm PQRS= 24cm²