ABCD is a parallelogram in which BC is produced to E such that CE = BC – InterviewSolution

InterviewSolution

1.	ABCD is a parallelogram in which BC is produced to E such that CE = BC. AE intersects CD at F. If `ar (DeltaDFB) = 3 cm^(2)`, then find the area of the parallelogram ABCD.
Answer» Correct Answer - `28 cm^(2)` `triangleMDA congMCP" " [therefore angleDMA = angleCMP, angleMDA=angleMCP, AD = CP " since " AD = BC and CP = BC]` `therefore DM = MC` (c.p.c.t) and so BM is a median of `triangleBDC`. Thus, `ar(DMB)=(1)/(2)ar(BDC)`. But, `ar(BDC)=(1)/(2)ar(ABCD)` [`therefore` BD is a diagonal of \|\|gm ABCD]. `therefore ar(DMB)=(1)/(4)ar(ABCD)` and so `ar(ABCD)= 28 cm^(2).

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