I tried using this formula
$$\int_a^bf(x)\sqrt{1+(f'(x))^2}dx$$
and managed to reduce the problem (after integrating by substitution twice) to: $$A=54(\pi)^2 \int_{46.32}^{-46.32} (\sec g)^3 \,dg$$ (where $u=\frac{3}{\pi}\tan g$, and $u=\cos (\frac{\pi}{3})x$. Now, to evaluate this I'll then have to use integration by parts which is, in this instant, quite unnecessarily tedious. So, I was wondering whether there is any quicker method to evaluate this. I have already thought of using Simpson's rule, but I don't believe that it is quite apt in this instant.
(Note:The answer Wolfram Alpha provided is $32.39$)