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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Sorry, could not draw the figure here. Steps to draw the figure-Draw IIgm PQRS with PS and QR as base. Join PR and QS. Now the solution is as follows:
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
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
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