Question

In the figure, PQRS is a Parallelogram, QS is the diagonal, A is the mid-point of SR and D is the mid-point of RQ. If the area of $△$ ASQ $=20$ cm${}^2$, then find the area of $△ARD$.

Answer 1

PQRS is a Parallelogram, QS is the diagonal
$\therefore ar\left(△RSQ\right)=2ar\left(△ASQ\right)=40{\text{cm}}^2$ [AQ is median of $△$ SRQ]
$\text{Area of}△ARD=\frac{1}{4}\text{[Area of}△SRQ]=\frac{40}{4}$ [AD is median of $△$ARQ]
$=10{\text{cm}}^2$