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A chord of a circle of radius $10\text{ cm}$ subtends an angle of $60^\circ$ at the centre O. Find the area of the shaded region. (Use $\sqrt{3} = 1.73, \sqrt{2} = 1.41$ and $\pi = 3.14$)
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Area of sector OAB $= \frac{60}{360} \times 3.14 \times 10^2 = \frac{314}{6}\text{ sq. cm}$ [$1$ mark]
Area of $\Delta OAB = \frac{\sqrt{3}}{4} \times 10^2 = \frac{173}{4}\text{ sq. cm}$ [$1$ mark]
Area of the shaded region $= \frac{314}{6} - \frac{173}{4} = \frac{109}{12}$ or $9.08\text{ sq. cm}$ [$1$ mark]
Area of $\Delta OAB = \frac{\sqrt{3}}{4} \times 10^2 = \frac{173}{4}\text{ sq. cm}$ [$1$ mark]
Area of the shaded region $= \frac{314}{6} - \frac{173}{4} = \frac{109}{12}$ or $9.08\text{ sq. cm}$ [$1$ mark]