A chord of a circle, of radius $\displaystyle 14$ cm, subtends an angle of $\displaystyle 60$° at the centre. Find the area of the smaller sector and perimeter of the smaller segment.

\(\displaystyle \therefore \triangle \mathrm{OAB}\) is an equilateral triangle. \(\displaystyle \Rightarrow \mathrm{AB}=14 c m\) Area of smaller sector \(\displaystyle =\frac{60}{360} \times \frac{22}{7} \times 14 \times 14\) \[=\frac{308}{3} c m^{2} \text { or } 102.6 c m^{2} \text { (approx.) } \] Perimeter of smaller segment \(\displaystyle =14+\frac{60}{360} \times 2 \times \frac{22}{7} \times 14\) \[=\frac{86}{3} \mathrm{~cm} \text { or } 28.6 \mathrm{~cm} \text { (approx.) } \]