ABCD is a parallelogram. P is the mid-point of AB. BD and CP intersect at Q such that CQ : QP = 3.1. If ar (ΔPBQ) = 10cm², find the area of parallelogram ABCD.

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Solution

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) =

And,

Area (BQC) =

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

Area (PCB) = …… (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.

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ABCD is a parallelogram. P is the mid-point of AB. BD and CP intersect at Q such that CQ : QP = 3.1. If ar (ΔPBQ) = 10cm2, find the area of parallelogram ABCD.

ABCD is a parallelogram. P is the mid-point of AB. BD and CP intersect at Q such that CQ : QP = 3.1. If ar (ΔPBQ) = 10cm², find the area of parallelogram ABCD.