Look; study your figure. Each side of that square ABCD is 2 x the
radius (r); each of those sides is 2r. Well, if you square 2r, that tells
you the area of the square is 4r2. Now, what we're subtracting
from that square is half of the circle. The area of the circle would be
pr2,
so 1/2 of it would be pr2/2;
therefore you have
4r2 - pr2/2.
As you factor the r2 out, you have the answer D, r2
(4 - p/2).