It helps to draw a radius in this diagram (Pillar II: Restating the given information). We are told in the narrative that the area is
so the radius must be 1. That means the side of the square is 2, resulting in an area of 4.
This is an easy one to guess without doing any work. The area of the square has to be slightly more than
or 3.14. That certainly eliminates A and B. The square isn't over twice as big as the circle. So that eliminates D and E, leaving only C!
Another wizardly technique would be to start with answer C and plug in. If the area of the square is 4, then each side has to be 2. If the side is 2, then the radius has to be 1. The area of a circle with a radius of 1 is
. C has to be right.