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

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

The area of a trapezium is $475 \, cm^2$ and the height is $19 \, cm$. Find the lengths of its two parallel sides if one side is $4 \, cm$ greater than the other.

Find the area of a triangular field,two sides of which are $510\,m$ and $520\,m$ and the perimeter is $1560\,m$. Also,find the cost of the field at the rate of Rs. $21$ per $m^2$.

In quadrilateral $ABCD$,$AB = 9 \, cm$,$BC = 13 \, cm$,$CD = 14 \, cm$,$DA = 12 \, cm$,and $BD = 15 \, cm$. Find the area of quadrilateral $ABCD$ in $cm^2$.

In $\Delta ABC$,$AB = 20 \, cm$,$BC = 48 \, cm$,and $AC = 52 \, cm$,find the area of $\Delta ABC$. (in $, cm^2$)