A circle of radius $3$ is centered at $A$. An equilateral triangle with side $5$ has a vertex at $A$. What is the difference between the area of the region that lies inside the circle but outside the triangle and the area of the region that lies inside the triangle but outside the circle?

1. The overlapping region cancels in the difference, so the answer is simply (circle area) $-$ (triangle area), regardless of how the two overlap.
2. $\pi(3)^2-\frac{\sqrt3}4(5)^2=9\pi-\frac{25\sqrt3}4$.
3. The answer is $\boxed{9\pi-\dfrac{25\sqrt3}4}$.