Question

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QUE: P and Q are any point lying on side DC and AD on a parallelogram ABCD . show that AREA OF APB = AREA OF BQC

Answer 1

If a parallelogram and a triangle are on

the same base and between the same parallels then area of the triangle is half

the area of the parallelogram.

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Given: In parallelogram ABCD, P & Q any two

points lying on the sides DC and AD.

To show:

ar (APB) = ar (BQC).

Proof:

Here, ΔAPB and ||gm ABCD stands on the same

base AB and lie between same parallel AB and DC.

Therefore,

ar(ΔAPB) = 1/2 ar(||gm ABCD) — (i)

Similarly,

Parallelogram ABCD and ∆BQC stand on the same

base BC and lie between the same parallel BC and AD.

ar(ΔBQC) = 1/2 ar(||gm ABCD) — (ii)

from eq (i) and (ii),

we have

 ar(ΔAPB)

= ar(ΔBQC)

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Hope

this will help you...

Answer 2

as they are on same base and same parallel there area are equal