Green Annulus

First, we'll add some radii to the concentric circles:

The area of the annulus is given by $\pi(R^2-r^2)=\pi x^2$ (using the Pythagorean Theorem)

By the cosine rule, $2x=\sqrt{3^2+5^2-2 \times 3 \times 5 \cos(120ᵒ)}=7$

$\therefore x=7/2$

$\implies$ area of annulus $=\pi (7/2)^2$

$=38.4845...$

$\boxed{=38.5}$ (3.s.f.)