If the area of an equilateral triangle is $16 \sqrt{3} \, cm^{2}$,then the perimeter of the triangle is (in $cm$)

Find the area of the trapezium $PQRS$ given in the figure.

The length of each side of an equilateral triangle having an area of $9 \sqrt{3} \text{ cm}^2$ is (in $\text{cm}$):

In quadrilateral $ABCD$,$AB = 20 \, cm$,$BC = 15 \, cm$,$CD = 12 \, cm$,$DA = 17 \, cm$ and $\angle B = 90^{\circ}$. Find the area of the quadrilateral in $cm^2$.

In the figure,$\Delta ABC$ has sides $AB = 7.5\, cm$,$AC = 6.5\, cm$,and $BC = 7\, cm$. On base $BC$,a parallelogram $DBCE$ of the same area as that of $\Delta ABC$ is constructed. Find the height $DF$ of the parallelogram (in $cm$).

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 $cm^2$.