Find the area of the shaded region. (Use π = 3.14 and √3 = 1.73205).

NCERT Class 10 Chapter 12

Page No. 236

Exercise 12.3

Question No. 10

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Let the each side of equilateral triangle = a

Area of equilateral triangle = 17320.5 cm²

⇒ √3/4 a² = 17320.5 ⇒ 1.73205/4 a² ⇒ 17320.5 ⇒ a² = 40000 ⇒ a = 200

Area of sector ADEF

= θ/360° × πr² = 60°/360° × 22/7(100)² = 1/6 × 3.14 × 100 × 100 = 15700/3 cm²

Area of shaded region = Area of equilateral triangle – Area of three sectors

= 17320.5 cm² – 3 x 15700/3 cm²

= 17320.5 cm² – 15700 cm²

= 1620.5 cm²