Hi Michael,

Suppose the radius of the circle is $r$ cm then in the diagram you sent the square has side length $2 \times r$ cm.

The shaded region is the square with the circle removed and hence the area of the shaded region is the area of the square minus the area of the circle. The area of the square is $(2 \times r)^2$ square centimeters and the area of the circle is $\pi \; r^2$ square centimeters. Thus

\[(2 \times r)^2 - \pi \; r^2 = 42 \mbox{ square centimeters.}\]

Solve for $r.$

Penny