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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