The sides of a triangle are $6 \, cm$,$8 \, cm$,and $10 \, cm$. The area of the triangle is ............. $cm^{2}$.

State whether the following statement is True or False and justify your answer:
The area of $\Delta ABC$ is $8 \, cm^2$ in which $AB = AC = 4 \, cm$ and $\angle A = 90^{\circ}$.

$PQRS$ is a square. If $PR = 10 \, cm$,then the area of $PQRS = \dots \, cm^2$.

Each side of an equilateral triangle measures $10\,cm$. Find the semi-perimeter of the triangle. (in $,cm$)

Find the cost of laying grass in a triangular field of sides $50 \, m$,$65 \, m$,and $65 \, m$ at the rate of $Rs \, 7$ per $m^2$ (in $Rs$).

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 $cm^2$.