A square is drawn inside a circle of radius 21 cm so that all four of its corners touch the circle. What is the area of the shaded region lying inside the circle but outside the square, in square cm? (Use π = 22/7.)

The circle has area $(22/7)\times 21^2=1386$ sq cm. The square's corners touch the circle, so its diagonal is the diameter, 42 cm, and a square of diagonal $d$ has area $d^2/2=1764/2=882$ sq cm. The shaded region = 1386 - 882 = 504 sq cm. The trap 882 reports the square itself rather than what is left around it; 1386 is the whole circle with the square never removed; 945 comes from taking the square's area as $r^2=441$, i.e. treating the radius as the side.