Question

In the adjoining figure, ABCD is a quadrilateral. A line through D, parallel to AC, meets BC produced in P. Prove that ar (△ ABP) = ar (quad. ABCD).

Answer 1

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).