Alright, so first we find the area of the whole circle using pi r squared
12^2 pi = 144 pi
Now we use the proportions of the sector and the whole circle:
30:360 (degrees; we will be using the same for the other ratio)
= x:144pi
1:12 = x:144
This basically equals
12x = 144
x = 12, and now we multiply pi, so 12 x 3.14 = 37.7 cm^2.
The first option is correct.