Quant OG Geometry Q9

[user2358]

I solved this correctly, but had two doubts:

1. If this question were a quantitative comparison question instead of single choice, then would we still assume that the shaded area would be 1/4 of the difference of area between the circle and inner square? Would we choose C (equal) if quantity B were 2 pi - 4 or would we choose D (can’t be determined) because the 1/4 assumption seems a bit shaky to me
2. Why is the outer square drawn here? Does it play any role?

[cylverixxx]

To answer 1), look at these 4 sectors that were created by said diagonals.

Are these segments "congruent’? The answer to this happens to be the answer to your question. In answering this, note that a square is a regular polygon.