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Question

In the given figure, ABCD and EFGD are two parallelogram and G is the mid-point of CD. Then ar(ΔDPC)=12ar(EFGD). Write True or False and justify your answer:
1795327_d57eb038ae8d43228dd9ce1ebd67fd82.png

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Solution

As ΔDPC and gmABCD are on the same base DC and between the same parallels AB and DC, So

ar(ΔDPC)=12ar(gm,ABCD) ....(1)

As, ar(EFGD)ar(ABCD)=DG×hDC×h=DG2DG=12 (G is the mid point of DC)

ar(EFGD)=12ar(ABCD)

So, ar(DPC)=ar(gmEFGD) (From (1))

Hence, the given statement is false.

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