The area of a sector formed by a $12\,cm$ long arc in a circle with radius $12\,cm$ is $\ldots \ldots \ldots \, cm^{2}$.

In $\odot(O, r)$,minor arc $\widehat{ABC}$ subtends a right angle at the centre. The area of the minor segment formed by $\widehat{ABC}$ is $14.25\,cm^2$ and the area of $\Delta OAC$ is $25\,cm^2$. Then,the area of the minor sector formed by $\widehat{ABC}$ is $\ldots \ldots \ldots cm^2$.

In a circle with radius $56 \, cm$,find the area of the minor sector,the major sector,and the minor segment corresponding to two radii perpendicular to each other.

In a circle with radius $14 \, cm$,$\overline{OA}$ and $\overline{OB}$ are radii perpendicular to each other. Then,the area of the minor sector corresponding to $\angle AOB$ is $\ldots \ldots \ldots \, cm^2$.

As shown in the diagram,$\overline{ OA }$ and $\overline{ OB }$ are two radii of $\odot( O , 21 \text{ cm} )$ perpendicular to each other. If $OD = 10 \text{ cm}$,find the area of the shaded region. (in $\text{cm}^2$)

The area of a minor sector of $\odot(P, 30)$ is $300 \, cm^2$. The length of the arc corresponding to it is .......... $cm$.