How to express this expression in terms of N? I am trying to express this formula in terms of N:
$$
A=\frac{a^2N} {a\cdot \tan{\frac{180}{N}}}
$$
I really don't know how to do this. I tried and got this:
$$
A \cdot a \cdot \tan{\frac{180}{N}} = a^2N
$$
$$
\tan{\frac{180}{N}}=\frac{a^2N}{Aa}
$$
$$
\frac{180}{N}=\tan^{-1}{\frac{a^2N}{Aa}}
$$
$$
N=\frac{180}{\tan^{-1}{\frac{a^2N}{Aa}}}
$$
But I just can't get the N on the right side. The $\tan$ is so annoying! How do I do this?

There is no way to to this. Many implicit equations, especially those involving trig functions, don't have any way to represent them explicitly.
You can use the approximation Andre points out to obtain $$N=\sqrt{\frac{A\pi}{a}}$$
