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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 3 = 1.73)

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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°)

=34AB2-60°360°π72+300°360°π72=34142-16×22772+56×22772=84.77-25.67+128.35=187.45 cm2
=34(AB)260°360°π(6)2+300°360°π(6)2=1.734(12)216×3.14(6)2+56×3.14(6)2=62.2818.84+94.2=137.64 cm2
Hence, the area of shaded region is 187.45 cm2

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