Regular Octagon Area Doing some maths homework I came across the area of a regular octagon on Google. This was given by:
$$ A=2(1+\sqrt{2})a^2 $$
I thought this looked rather ugly and slightly complicated and so began to look at regular octagons myself (Yes, I'm a nerd :)!). I managed to re-write the equation to
$$ A=\frac{x^2} {\sqrt{2}\cdot\sin^2(22.5)} $$
I could not find this equation anywhere on the internet so I don't know if it's correct. Has it been discovered before? Is it correct?
Thank you,
       Sam.

P.S. I could post the proof if you need it?

Assuming that $a$ and $x$ are both the length of one side of the regular octagon, the results are the same:
$$\frac{1}{\sqrt{2} \sin^2 (\pi/8)} = \frac{1}{\sqrt{2}} \left(\frac{2}{1 - \cos(\pi/4)}\right) = \frac{\sqrt{2}}{1 - \frac{1}{\sqrt{2}}} = 2(1 + \sqrt{2}).$$
The area formula for the general regular $n$-gon just follows from dividing it into $n$ congruent triangles.
