i put "diameter² = 8" , not diameter=8 :p
but yeah, in fact i didn"t know the name for root in english xD sorry^^
the problem in my logic is that:
radius² = 2 and not 4, since you divide by 2² and not only by 2, my bad :)
so the answer is:
area full circle = 2pi
2pi - 4 for the area circle-area square
pi -2 is the answer :D

(btw, if i couldn't post two answers, I can delete my com if you want :))