It would help to plot it first.
!enter image description here
Now use this formula $$A = \frac{1}{2}\int_{\alpha}^{\beta}f(\theta)^2\ d\theta$$
From the picture we see that the curve runs from $0$ to $2\pi$
$$A = \frac{1}{2}\int_{0}^{2\pi}(3 + \sin(\theta))^2\ d\theta = \frac{19\pi}{2}$$ The computation is trivial and it's something you can look up on WolframAlpha if you aren't sure