In $Fig.$,$ABCD$ is a square of side $14 \, cm$. With centres $A, B, C$ and $D$,four circles are drawn such that each circle touches externally two of the remaining three circles. Find the area of the shaded region (in $cm^2$). $\left[\text{Use } \pi = \frac{22}{7}\right]$

In a circular table cover of radius $32 \, cm$,a design is formed by leaving an equilateral triangle $ABC$ in the middle as shown in the figure. Find the area of the design. [Use $\pi = \frac{22}{7}$]

$A$ car has two wipers which do not overlap. Each wiper has a blade of length $25 \, cm$ sweeping through an angle of $115^{\circ}.$ Find the total area cleaned at each sweep of the blades. [use $\pi=\frac{22}{7}$]

The area of an equilateral triangle $ABC$ is $17320.5 \, cm^2$. With each vertex of the triangle as a centre,a circle is drawn with a radius equal to half the length of the side of the triangle (see figure). Find the area of the shaded region in $cm^2$. (Use $\pi = 3.14$ and $\sqrt{3} = 1.73205$)

Find the area of the shaded region in the figure if $ABCD$ is a square of side $14 \, cm$ and $APD$ and $BPC$ are semicircles. (in $cm^2$) [Use $\pi = \frac{22}{7}$]

The radii of two circles are $8 \, cm$ and $6 \, cm$ respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles. [use $\pi = \frac{22}{7}$] (in $cm$)