If the area of a triangle whose base is $6\, cm$ is equal to the area of a circle of radius $6\, cm$,then find the height of this triangle (in $cm$).

In the given figure,$OP = PQ = 14 \, cm$ and semicircles are drawn on $OP$,$PQ$,and $OQ$ as diameters. Then,the perimeter of the shaded area is . . . . . . $cm$.

$A$ field is in the shape of a parallelogram. Its adjacent sides and one diagonal are $65 \, m$,$119 \, m$,and $156 \, m$ respectively. Find the cost of gravelling it at the rate of $₹ 10$ per $m^2$ (in $Rs.$).

$A$ rectangular sheet of cardboard is of $4 \, cm \times 2 \, cm$. If a circle of the greatest possible area is cut from it,then the area of the remaining portion is:

The perimeter of a right triangle is $12 \, cm$. The hypotenuse is $5 \, cm$. What are the other two sides and the area of the triangle?

$A$ vessel is in the form of a hollow cylinder mounted on a hemispherical bowl. The diameter of the hemisphere is $14 \, cm$ and the total height of the vessel is $13 \, cm$. Find the capacity of the vessel in $cm^3$. (Take $\pi = 22/7$)