2019 AMC 12B Question 24

Let $\omega=-\dfrac12+\dfrac12 i\sqrt3.$ Let $S$ denote all points in the complex plane of the form $a+b\omega+c\omega^2,$ where $0\le a\le1,$ $0\le b\le1,$ and $0\le c\le1.$ What is the area of $S?$