Question

Why are the areas of unshaded regions in the two figures equal?

• A. The radius of the quarter circles in figure 1 is equal to the radius of the circle in figure 2
• B. None of the above
• C. The radii of the quarter circles are equal.
• D. Both A and B

Answer 1

The correct option is D

Both A and B

The two areas are equal because the four quarter circles in the first figure have the same radius as the circle. The area of shaded region in the first figure is the area of the square without the four quarter circles (marked as 1,2,3 and 4), and the area of the shaded region in the second figure is the area of the square without the circle. Also, the radii of the quarter circles 1,2,3 and 4 are equal.