What is the area of the shaded region in sq. cm?

In the given figure, each side of the square is 2 m long. Four semicircles are drawn inside the square taking each of the sides as diameter. Thus a flower of four petals is formed which is shown by shading. What is the area of the shaded region in sq. cm?

SET-A Q.no. 104

  1. 2π-4
  2. 4-2π
  3. 4-π
  4. π-4
Anurag Mishra Professor Asked on 17th December 2015 in Maths.
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  • 1 Answer(s)

    Answer:  (1) 2 pai – 4 

    Solution:-
    The side of the square  = 2 cm = diameter of the circle
    Then radius of the circles = 2/2 = 1 cm 

    According to the question, In the figure

    RE: What is the area of the shaded region in sq. cm?


    Now, the area of circle = Pai x 1 x 1
    Then  area of the quarter circle = Pai/4

    The are of the triangle = 1/2
    Thus, the area of the half leaf = Pai/4 – 1/2

    Therefore, the area of four leaves = 8 (Pai/4 – 1/2)
      2 pai – 4

    Hence, the correct answer is option (1) 2 pai – 4.  

    Anurag Mishra Professor Answered on 17th December 2015.
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