AMC 12 2002b Problem 25

Let $f(x) = x^2 + 6x + 1$, and let $R$ denote the set of points $(x,y)$ in the coordinate plane such that $$f(x) + f(y) \le 0 \text{and} f(x)-f(y) \le 0$$ The area of $R$ is closest to

$\mathrm{(A)}\ 21 \mathrm{(B)}\ 22 \mathrm{(C)}\ 23 \mathrm{(D)}\ 24 \mathrm{(E)}\ 25$