105
AB and CD are diameters of a circle with centre O and radius $7 \text{ cm}$. If $\angle BOD = 30^\circ$, then find the area and perimeter of the shaded region.
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Area of the shaded region $= 2 \left( \frac{30}{360} \times \frac{22}{7} \times 7 \times 7 \right) = \frac{77}{3} \text{ sq. cm or } 25.67 \text{ sq. cm}$ ($1 + \frac{1}{2}$ marks)
Perimeter of the shaded region $= 2 \left( 14 + \frac{30}{360} \times 2 \times \frac{22}{7} \times 7 \right) = \frac{106}{3} \text{ cm or } 35.33 \text{ cm}$ ($1 + \frac{1}{2}$ marks)
Perimeter of the shaded region $= 2 \left( 14 + \frac{30}{360} \times 2 \times \frac{22}{7} \times 7 \right) = \frac{106}{3} \text{ cm or } 35.33 \text{ cm}$ ($1 + \frac{1}{2}$ marks)