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In a figure, PQRS and EFRS are two parallelograms then, prove that ar (MFR) = 1/2ar (PQRS).

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Best answer

PQRS and EFRS are on the same base SR and between the same parallels EF and SR. 

So their areas are equal

i.e. ar (PQRS) = ar (EFRS) ….(i)

Also ar (∆MFR) = \(\frac { 1 }{ 2 }\) ar (EFRS) …(ii)

From equation (i) and (ii), we get

ar (MFR) = \(\frac { 1 }{ 2 }\) ar (PQRS).

Hence proved.

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