Find the area of a circle inscribed in an equilateral triangle of side 18 cm.

The shape of the top of a table in a restaurant is that of a segment of a circle with centre O and ∠BOD = 90°. BO = OD = 60 cm. Find :

(i) the area of the top of the table;

(ii) the perimeter of the table.

In the given figure, ABCD is a rectangle inscribed in a circle. If two adjacent sides of the rectangle be 8 cm and 6 cm, calculate :

(i) the radius of the circle; and

(ii) the area of the shaded region.

Calculate the area of the shaded region, if the diameter of the semi-circle is 14 cm.