Where a circular arc of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm as centre.
NCERT Class 10 Math’s Chapter 12
Page No. 235
Exercise 12.3
Question No. 4
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We know that each angle of equilateral triangle is 60°.
Area of sector OCDE
= 60°/360° × πr² = 1/6 × π(6)² = 1/6 × 22/7 × 6 × 6 = 132/7 cm²
Area of equilateral triangle OAB
= √3/4 (12)² = 36√3 cm²
Area of circle
= πr² = π(6)² = 22/7 × 6 × 6 = 792/7 cm²
Area of shaded region
= Area of circle + Area of triangle OAB- Area of sector OCDE
= (792/7 + 36√3 – 132/7) cm²
= (36√3 + 660/7) cm²
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