Question

ABCD is a quadrilateral such that AC parallel to DP. Prove that ar(ABCD) = ar (Triangle ABP).

Answer 1

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Answer 2

Answer:

From the figure we know that △ ACP and △ ACD lie on the same base AC between parallel lines AC and DP

It can be written as

Area of △ ACP = Area of △ ACD

By adding △ ABC to both LHS and RHS

Area of △ ACP + Area of △ ABC = Area of △ ACD + Area of △ ABC

So we get

Area of △ ABP = Area of quadrilateral ABCD Therefore, it is proved that ar (△ ABP) = ar (quad. ABCD).

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