If the area of the shaded region is, then what is the radius of the whole sector?

cm^{2}

The shaded region is the difference of the sector and the right isosceles triangle. Let’s assume the radius of the sector is r, so its area is

.

If we draw the height of the triangle from the hypotenuse, the height is r/2. Thus, the area of the right triangle is

.

Thus, the area is represented as

.

Eliminating from both sides of the
equation,
we have , so = 4 cm. We see that 4^{2}/4
also equals 4 so it works.