Jerry1982 wrote:

hi ,

will this type of question appear on GMAT?

also i was unable to understand the solution , can you please explain this in detail.

Try making the diagram from the given diagram. You are given that "Square ABCD has arc AC centred at B & arc BD centred at C". So make the circle centered at B and the circle centered at C. Now, remove the lines of the square that you don't care about and focus on only the shaded area. Don't worry about the way I have named the vertices - they are not according to the given diagram. Just note that the shaded portion corresponds to the area bounded by arc AC, arc BC and line BA in my diagram. Now join the points that define the shaded region to get an equilateral triangle (they are all radii of circles with equal radii).

Then you get that the angle subtended at the center is 60 degrees which means area of the sector is 1/6th (which is 60/360) of the area of the circle. But that is not all the shaded region. There is some extra shaded region lying between arc BC and line BC (in my diagram). To get the value of this, we subtract the area of the triangle BAC from the area of the sector BAC (in my diagram)

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