2018 · Q95
What is the area of the region bounded internally by a square of side of length ‘a’ and externally by a circle passing through the four corners of the square?
Elementary MathematicsMensuration
- A(π - 1)a² square units
- B(π - 1)a²/2 square units
- C(π - 2)a² square units
- D(π - 2)a²/2 square units
Explanation
The circumradius is half the diagonal, a/√2, so the circle's area is πa²/2. The region between circle and square is πa²/2 − a² = (π − 2)a²/2, option (D).