An equilateral triangle has side length $8$. What is the area of the region containing all points that are outside the triangle but not more than $2$ units from a point on the triangle?

1. The shape consists of $3$ rectangles (each side-length by radius) and one full circle of that radius: area $=3sr+\pi r^2$.
2. With $s=8, r=2$: area $=3(8)(2)+\pi(4)=48+4\pi$.
3. The answer is $\boxed{48+4\pi}$.