Area of a rectangle $=$ ............

All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?

In $\Delta PQR$,$PM$ is a median and $N$ is the midpoint of $PM$. If $\text{ar}(PQN) = 36 \text{ cm}^2$,then $\text{ar}(PQR) = \dots \text{ cm}^2$.

In quadrilateral $ABCD$,the angles are in the ratio $\angle A : \angle B : \angle C : \angle D = 2 : 4 : 5 : 7$. Find the measure of each angle of the quadrilateral and state the type of quadrilateral $ABCD$.

In quadrilateral $ABCD$, one of its diagonals $AC$ measures $20 \, cm$. The altitudes on $AC$ from vertices $B$ and $D$ are $8 \, cm$ and $12 \, cm$ respectively. Find the area of quadrilateral $ABCD$ in $cm^2$.

Through $A, B$ and $C$,lines $RQ, PR$ and $QP$ have been drawn,respectively parallel to sides $BC, CA$ and $AB$ of a $\triangle ABC$ as shown in the figure. Show that $BC = \frac{1}{2} QR$.