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in Parallelograms by (58.8k points)

If P and Q are any two points lying respectively on the sides DC and AD of a parallelogram ABCD then show that ar (△ APB) = ar (△ BQC).

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From the figure we know that △ APB and parallelogram ABCD lie on the same base AB and between the same parallels AB and DC

So we get

Area of △ APB = ½ (Area of parallelogram ABCD) …….. (1)

In the same way △ BQC and parallelogram ABCD lie on the same base BC and between the same parallels BC and AD

So we get

Area of △ BQC = ½ (Area of parallelogram ABCD) …….. (1)

Using the equations (1) and (2)

We get

Area of △ APB = Area of △ BQC

Therefore, it is proved that Area of △ APB = Area of △ BQC.

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