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Mridul Gupta
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Asked: 2023-02-23T08:44:01+00:00 In:

The area of an equilateral triangle ABC is 17320.5 cm². With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see Figure).

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The area of an equilateral triangle ABC is 17320.5 cm². With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see Figure).

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

chapter 12mathematicsncert class 10
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      The area of an equilateral triangle ABC is 17320.5 cm². With each vertex of the triangle as centre, a circle is drawn with radius equal to half the length of the side of the triangle (see Figure).

      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

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