Question

In parallelogram ABCD, P is a point on side AB and Q is a point on side BC.
Prove that :$\Delta$ CPD and $\Delta$ AQD are equal in area.

Answer 1

Given ABCD is a parallelogram, P and Q are any point on side AB and BC respt.

Join diagonal AC and BD

Area of $\Delta$ CPD = Area of $\Delta$ BCD ( Area of triangle with same base and between same set of parallel line )

Area of $\Delta$ BCD= $\frac{1}{2}$ Area of parallelogram ABCD( Diagonal of parallelogram bisect it into two equal part)

Then area of $\Delta$ CPD = $\frac{1}{2}$ Area of parallelogram ABCD

Similarly area of $\Delta$ AQD=area $\Delta$ ABD=$\frac{1}{2}$ Area of parallelogram ABCD

Hence the area of $\Delta$ CPD =area of $\Delta$ AQD