If the area of the shaded region is, then what is the radius of the whole sector?
The shaded region is the difference of the sector and the right isosceles triangle. Lets 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 42/4 also equals 4 so it works.