Bunuel wrote:

Since the radius of the big circle (\(\frac{\pi}{2}\)) is twice the radius of the inscribed circle (\(\frac{\pi}{4}\)) then its area is 4 times greater than the area of the inscribed circle (because in the area formula the radius is squared.

Bunuel wrote:

Thus the area of the semicircle is \(\frac{4}{2}=2\) times greater than the area of the inscribed circle

Took me a while but I finally understand this. I originally solved this algebraically but that takes too long. It's better to use the area ratio information.

(Radius Big Circle/ Radius Inner Circle) = (pi/2) / (pi/4) = 2/1

(Area Big Circle/ Area Inner Circle) = (2/1)^2 = 4/1

(Area Semicircle / Area Inner Circle) = 4/1 * 1/2 = 2/1 <-- answer