Faster method:

Diameter of 8 means square has side length 8
8^2=64
Clearly, we see that there's only 3/4ths of a square there
64*3/4=48
Can only be C or D
3 semicircle shapes remaining=X of (X+48) must be divisible by 3
Only C has the X portion divisible by 3; no need to spend time actually calculating semicircle portions.

You can answer this question less than a minute without using a calculator: At first glance, we can see we have 3/4 or 0.75 of the square and 1.5 circles in the figure. Side of the square is equal to the diameter of the circle, which is 8. By looking at the answer choices we can see the area of the square and circles are separated, which is the bonus point. So, the area of the shaded square is: 0.75 x 8 x 8 = 48, instantly we can erase 3 answer choices and left with C and D. Now, we just need to find the area of our 1.5 circle with diameter of 8 or radios of 4. Forget about the Pi (3.14) and we have: 1.5 x 4 x 4 = 24
Hence, the answer choice is C