Question

In adjoining fig. MNPQ and ABPQ are parallelogram and T is any point on the side BP. prove that .1)ar(MNPQ) =ar(ABPQ).2)ar(ATQ)=1÷2ar(MNPQ)
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Answer 1

From the given figure we know that △ATQ and parallelogram ABPQ lie on the same base AQ and between the same parallels AQ and BP.

so we get

Area of △ATQ=1/2 ( Area of parallelogram ABPQ)

Therefore, it is proved that ar(△ATQ)=1/2 ar(MNPQ).