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Find the area of the shades segments in the figure

Find the area of the shades segments in the figure
  • A.
    (sqrt{3}
  • B.
    4 (pi – sqrt{3})
  • C.
    -(frac{2}{3} pi)
  • D.
    (frac{2pi}{3}) -3
Correct Answer: Option D
Explanation

Area of section = (frac{60^o}{360^o}) x 11r2
= (frac{60}{360} times pi times 2^2)
= (frac{1}{6}) x 4
= (frac{4pi}{6})
= (frac{2pi}{3})
Area of triangle = (frac{1}{2x})
= 2 x 28…….60
Segment Area = Area of section – Area of triangle
= (frac{2pi}{3}) -3