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Question
Find the area of a shaded region in the the following figure,where a circular arc of radius 7 cm has been drawn with vertex A of an equilateral triangle ABC of side 14 cm as centre. (Use π = 22/7 and \[\sqrt{3}\] = 1.73)
Solution
In equilateral traingle all the angles are of 60°
∴ ∠BAC = 60°
Area of the shaded region = (Area of triangle ABC − Area of sector having central angle 60°) + Area of sector having central angle (360° − 60°)
\[= \frac{\sqrt{3}}{4} \left( AB \right)^2 - \frac{60°}{360°}\pi \left( 7 \right)^2 + \frac{300°}{360°}\pi \left( 7 \right)^2 \]
\[ = \frac{\sqrt{3}}{4} \left( 14 \right)^2 - \frac{1}{6} \times \frac{22}{7} \left( 7 \right)^2 + \frac{5}{6} \times \frac{22}{7} \left( 7 \right)^2 \]
\[ = 84 . 77 - 25 . 67 + 128 . 35\]
\[ = 187 . 45 {cm}^2\]
Hence, the area of shaded region is 187.45 cm2
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