The length of a diagonal of a square is $6$. Then,its area is............

The ratio of the areas of $\odot(O, 6)$ and $\odot(P, 12)$ is ...........

The radius of a semicircular garden is $35 \, m$. One has to walk $\ldots \ldots \ldots \ldots \, m$ to make one complete round of that garden.

Circumferences of two circles are equal. Is it necessary that their areas be equal? Why?

In the given diagram,$\Delta ABC$ is a right-angled triangle in which $m \angle B = 90^{\circ}$ and $AB = BC = 14 \text{ cm}$. $A$ minor sector $BAPC$ is a sector of a circle with center $B$ and radius $BA$. $A$ semicircle arc $\widehat{AQC}$ is drawn on diameter $\overline{AC}$. Find the area of the shaded region in $\text{cm}^2$.

From a circular metallic sheet with radius $21\, cm$,a regular hexagon of side $21\, cm$ is cut off. Find the area of the remaining sheet. $(\sqrt{3} = 1.73)$ (in $cm^2$)