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 
, what is the perimeter of the square?
- 24
- 72
The correct answer is:
HINT: Observe the figure and find out the perimeter.
Complete step by step Solution
Given that the area of shaded region is 
Here it's clear that area of whole circle is 
and area of that square is 
.
From this, we can say that radius r = 6. [since area of circle is ]
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 
Then on simplification, we get 
.
We know that perimeter of a square is 4 times its side(here 
).
So perimeter = 
.
We get perimeter to be .
Hence option C is the correct answer.
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