In a right-angled triangle,find the hypotenuse if the base and perpendicular are respectively $36015 \ cm$ and $48020 \ cm$.

The area of a ring whose outer and inner radii are respectively $20 \, cm$ and $15 \, cm$ is? (in $cm^2$)

Three circles of radius $21 \, cm$ are placed in such a way that each circle touches the other two. What is the area of the portion enclosed by the three circles? (in $sq \cdot cm$)

The radius and vertical height of a cone are $5 \text{ cm}$ and $12 \text{ cm}$ respectively. Then its lateral surface area is? (in $\text{cm}^2$)

In the given figure,$PB$ is one-third of $AB$ and $BQ$ is one-third of $BC.$ If the area of $BPDQ$ is $20 \, cm^{2},$ then what is the area (in $cm^{2}$) of $ABCD$?

In the given figure, $ABCDEF$ is a regular hexagon whose side is $6\, cm$. $APF$, $QAB$, $DCR$, and $DES$ are equilateral triangles. What is the area (in $cm^2$) of the shaded region (in $\sqrt{3}$)?