If $\theta$ is the angle (in degrees) of a sector of a circle of radius $r$,then the area of the sector is:

In a circle with radius $42\,cm$,an arc subtends an angle of measure $120^{\circ}$ at the centre. Then,the area of the minor sector formed by that arc is $\ldots \ldots \ldots \,cm^{2}$.

As shown in the diagram,$\triangle ABC$ is an equilateral triangle in which $BC = 70 \, cm$ and $P$ and $R$ are midpoints of $\overline{AB}$ and $\overline{AC}$ respectively. $\widehat{PQR}$ is an arc of $\odot(A, AP)$. Find the area of the shaded region. $(\sqrt{3} = 1.73)$ (in $cm^2$)

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

The areas of two sectors of two different circles are equal. Is it necessary that their corresponding arc lengths are equal? Why?

As shown in the diagram,$\overline{OA}$ and $\overline{OB}$ are two radii of $\odot(O, 35 \text{ cm})$ perpendicular to each other. If $OD = 12 \text{ cm}$,find the area of the shaded region. (in $\text{cm}^2$)