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

 

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Solution.

Given: Two parallelograms ABCD and AEFD.

To prove: ar(PEA)=ar(QFD)

Proof:

PQDA is a parallelogram, so APDQ,PQAD

Now, parallelograms PQDA and AEFD are on the same base AD and lie between the same parallel lines AD and EQ .

Hence,

ar(gmPQDA)=ar(gmAEFD)ar(PFDA)+ar(QFD)=ar(PEA)+ar(PFDA)

So, we get:

ar(QFD)=ar(PEA)

Hence proved

 

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