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  • In Fig., ABCD and AEFD are two parallelograms. Prove that ar (PEA) = ar (QFD)

In Fig., ABCD and AEFD are two parallelograms. Prove that ar (PEA) = ar (QFD)

Answers (1)

Solution.

Given: Two parallelograms ABCD and AEFD.
To prove: ar(\triangle PEA) = ar(\triangle QFD)
Proof:
PQDA is a parallelogram, so AP \parallel DQ, PQ \parallel AD
Now, parallelograms PQDA and AEFD are on the same base AD and lie between the same parallel lines AD and EQ. Hence,
ar(\parallel gmPQDA)=ar(\parallel gmAEFD)
ar(PFDA)+ar(\triangle QFD)=ar(\triangle PEA)+ar(PFDA)
So, we get:
ar(\triangle QFD) = ar(\triangle PEA)
Hence proved

 

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