$A$ chord of a circle of radius $12 \, cm$ subtends an angle of $120^{\circ}$ at the centre. Find the area of the corresponding segment of the circle. (in $cm^2$)
(Use $\pi = 3.14$ and $\sqrt{3} = 1.73$)

Find the area of the segment $AYB$ shown in the figure if the radius of the circle is $21 \, cm$ and $\angle AOB = 120^{\circ}$. (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 $\sqrt{3} = 1.73205$)

The wheels of a car have a diameter of $80\, cm$ each. How many complete revolutions does each wheel make in $10\, minutes$ when the car is travelling at a speed of $66\, km/h$? [Use $\pi = \frac{22}{7}$]

Find the area of the shaded region in the figure,where $ABCD$ is a square of side $14 \, cm$. (in $cm^2$)

The figure depicts a racing track whose left and right ends are semicircular.
The distance between the two inner parallel line segments is $60 \, m$ and they are each $106 \, m$ long. If the track is $10 \, m$ wide,find:
$(i)$ the distance around the track along its inner edge
$(ii)$ the area of the track. $\left[ \text{Use } \pi = \frac{22}{7} \right]$