Answer 1

It is given that CQ : QP = 3: 1 and Area (PBQ) = 10 cm²

Let CQ = x and QP = 3x

We need to find area of the parallelogram ABCD.

From the figure,

Area (PBQ) = `1/2 xx x xx h = 10 ⇒ x xx h = 20`

And,

Area (BQC) = `1/2 xx 3x xx h = 30   cm^2` 

Now, let H be the perpendicular distance between AP and CD. Therefore,

Area (PCB) = `1/2 PB xx H = 30  cm^2`  …… (1)

Thus the area of the parallelogram ABCD is,

Area (ABCD) = AB × H

⇒ Area (ABCD) = 2BP × H

From equation (1), we get

Area (ABCD) = 4 × 30 = 120 cm²

Hence, the area of the parallelogram ABCD is 120 cm²