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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 Fig. 12.28). Find the area of the shaded region. (Use π = 3.14 and √3 = 1.73205). Q.10

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Give me the ncert class 10 solution of chapter ares related to circles .Find the best and easiest way t0 solve this question . Sir please help me to find the exercise 12.3 question no. 10 . 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 Fig. 12.28). Find the area of the shaded region. (Use π = 3.14 and √3 = 1.73205).

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  1. ABC is an equilateral triangle.

    ∴ ∠ A = ∠ B = ∠ C = 60°

    There are three sectors each making 60°.

    Area of ΔABC = 17320.5 cm2

    ⇒ √3/4 ×(side)2 = 17320.5

    ⇒ (side)2 =17320.5×4/1.73205

    ⇒ (side)2 = 4×104

    ⇒ side = 200 cm

    Radius of the circles = 200/2 cm = 100 cm

    Area of the sector = (60°/360°)×π rcm2

    = 1/6×3.14×(100)cm2

    = 15700/3cm2

    Area of 3 sectors = 3×15700/3 = 15700 cm2

    Thus, area of the shaded region = Area of equilateral triangle ABC – Area of 3 sectors

    = 17320.5-15700 cm= 1620.5 cm2

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