Question

In the adjoining figure, a parallelogram ABCD is shown in which P divides AB in the ratio 1 : 2. If the area of the parallelogram ABCD is 60 cm², then area (BPDC) is:

Options

• 20 cm²

• 40 cm²

• 50 cm²

• 30 cm²

Answer 1

50 cm²

Explanation:

Let AP : PB = 1 : 2.

So, `AP = 1/3 AB`.

The triangle APD and the parallelogram ABCD share the same altitude.

So, `"area" (APD) = 1/2 xx AP xx h`

= `1/2 xx (1/3 AB) xx h` 

= `1/6 (AB xx h)`

= `1/6 xx 60`

= 10 cm²

Removing this triangle from the whole parallelogram gives area (BPDC)

= 60 – 10

= 50 cm²