Find the area of the segment $A Y B$ shown in fig $12.9$ , if radius of the circle is $21 c m$ and $∠ A O B = 120^{o} . (u s e π = \frac{22}{7})$

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Solution

Area of sector AYB $= \frac{π r^{2}}{360} \times 120 = \frac{π r^{2}}{3}$
Area of $Δ$ AOB $= \frac{1}{2} (O A) (O B) sin θ = \frac{1}{2} (21)^{2} \times \frac{\sqrt{3}}{2}$
$=$ Area of shaded region $= \frac{π (21)^{2}}{3} - \frac{\sqrt{3}}{4} (21)^{2}$
$= (21)^{2} [\frac{22}{21} - \frac{\sqrt{3}}{4}] = 271.04 c m^{2}$

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