$ABCDEF$ is a regular hexagon with centre $\mathrm{O}$ as shown in the figure. If the area of the triangle $OAB$ is $9{\mathrm{cm}}^2$, find the area of the circle in which the hexagon is inscribed.

Four equal circles, each of radius $5 \mathrm{cm}$, touch each other as shown in the following figure. Find the area included between them (Take $\mathrm{\pi }=3.14$).

Four equal circles, each of radius$a$, touch each other. Show that the area between them is $\frac{6}{7}{a}^2 {\mathrm{cm}}^2$ (Take $\mathrm{\pi }=\frac{22}{7}$).

A child makes a poster on a chart paper drawing a square $\mathrm{ABCD}$ of side $14 \mathrm{cm}$. She draws four circles with centre$\mathrm{A}, \mathrm{B}, \mathrm{C}$ and$\mathrm{D}$ in which she suggests different ways to save energy. The circles are drawn in such a way that each circle touches externally two of the three remaining circles (in the following figure). In the shaded region she write a message 'Save Energy'. Find the perimeter and area of the shaded region (Use $\mathrm{\pi }=\frac{22}{7}$).

The diameter of a coin is $1 \mathrm{cm}$ (Fig. $13.49$). If four such coins be placed on a table so that the rim of each touches that of the other two, find the area of the shaded region (Take $\mathrm{\pi }= 3.1416$).

In Fig., $\mathrm{AB}$ and $\mathrm{CD}$ are two diameters of a circle perpendicular to each other and $\mathrm{OD}$ is the diameter of the smaller circle. If$\mathrm{OA}=7 \mathrm{cm}$, find the area of the shaded region. (Take $\pi =\frac{22}{7}$)

In Fig $13.96$, $\mathrm{PSR}$, $\mathrm{RTQ}$and $\mathrm{PAQ}$are three semicircles of diameter $10 \mathrm{cm}$,$3 \mathrm{cm}$ and $7 \mathrm{cm}$ respectively. Find the perimeter of shaded region.

In Fig., two circles with centres $\mathrm{A}$ and $\mathrm{B}$ touch each other at the point$\mathrm{C}$ . If $\mathrm{AC}=8 \mathrm{cm}$ and $\mathrm{AB}=3 \mathrm{cm}$, find the area of the shaded region.