Maths-
General
Easy

Question


In the figure shown, point O is the center of the circle. One vertex of the square lies on the circle, and the opposite vertex is point O. If the area of the shaded region is 36 pi minus 18, what is the perimeter of the square?

  1. 24  
  2. 72  
  3. 12 square root of 2  
  4. 36 square root of 2  

The correct answer is: 12 square root of 2


    HINT: Observe the figure and find out the perimeter.
    Complete step by step Solution

    Given that the area of shaded region is 36 pi minus 18.
    Here it's clear that area of whole circle is 36 pi and area of that square is 18.
    From this, we can say that radius r = 6. [since area of circle is 36 pi]
    Draw a diagonal in that square and it will be 6 units which is the actual radius of the circle.
    The diagonal splits the square into 2 triangles and the diagonal acts as the hypotenuse.
    Let sides of the square be x.
    Since it is a square, all the angles are right angles.
    By pythagoras theorem, we have 2 x to the power of 2 end exponent equals 36
    Then on simplification, we get x equals 3 square root of 2.
    We know that perimeter of a square is 4 times its side(here x).
    So perimeter = 4 x equals 4 cross times 3 square root of 2 equals 12 square root of 2.
    We get perimeter to be 12 square root of 2.
    Hence option C is the correct answer.

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