The sides of $\Delta PQR$ measure $13 \, cm$, $14 \, cm$, and $15 \, cm$. Find its area in $cm^2$.

$A$ triangle and a parallelogram have the same area. If the sides of the triangle are $10 \, cm$,$17 \, cm$,and $21 \, cm$,and the parallelogram stands on the base $12 \, cm$,find the height of the parallelogram. (in $, cm$)

In a kite-shaped quadrilateral $ABCD$,$AB = AD = 12 \, cm$,$CB = CD = 17 \, cm$,and $AC = 25 \, cm$. Find its area and the length of diagonal $BD$.

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

$A$ floral design on a floor is made up of $16$ tiles which are triangular,the sides of the triangle being $9\, cm, 28\, cm$ and $35\, cm$ (see Fig.). Find the cost of polishing the tiles at the rate of $50p$ per $cm^2$.

In quadrilateral $ABCD$, $\angle A = 90^{\circ}$, $AB = 15 \text{ cm}$, $BC = 25 \text{ cm}$, $CD = 12 \text{ cm}$, and $DA = 8 \text{ cm}$. Find the area of quadrilateral $ABCD$. (in $\text{ cm}^2$)