Let \omega=-\dfrac{1}{2}+\dfrac{1}{2} i \sqrt{3}. Let S denote all points in the complex plane of the form a+b \omega+c \omega^{2}, where 0 \leq a \leq 1,0 \leq b \leq 1, and 0 \leq c \leq 1. What is the area of S ?
Answer Choices
A. \dfrac{1}{2} \sqrt{3}
B. \dfrac{3}{4} \sqrt{3}
C. \dfrac{3}{2} \sqrt{3}
D. \dfrac{1}{2} \pi \sqrt{3}
E. \pi