Question

In the given figure, ABCD is a parallelogram. P and Q are any two points in AB and BC respectively. Area of $\Delta$ ADQ= ___

• A. area $\Delta ADP$
• B. area $\Delta DPC$
• C. area $\Delta PBC$
• D. area ||gm ABCD.

Answer 1

The correct option is B area $\Delta DPC$

(i)ABCD is a ||gm (given)

$\left(ii\right)area\Delta ADQ=\frac{1}{2}Area||gmABCD$

(Area of a triangle is half the area of ||gm if they are on the same base (AD) and between the same ||'s)

$\left(iii\right)area\Delta DPC=\frac{1}{2}Area||gmABCD$
(Area of a triangle is half the area of ||gm if they are on the same base (DC) and between the same parallels)

$\left(iv\right)\therefore area\Delta ADQ=area\Delta DPC$