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

The sides of a triangular plot are in the ratio of $4: 7: 9$ and its perimeter is $500 \, m$. Find its area.

The sides of a triangle are $a \, cm$,$b \, cm$,and $c \, cm$. Also,its semi-perimeter is $s \, cm$. If $s - a = 10 \, cm$,$s - b = 15 \, cm$,and $s - c = 12 \, cm$,then $s = \dots \, cm$.

The shape of a plot is a rhombus. Its perimeter is $340 \, m$ and one diagonal is $72 \, m$. Find its area. (in $, m^2$)

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

The perimeter of an isosceles triangle is $32 \, cm$. The ratio of the equal side to its base is $3:2$. Find the area of the triangle.