What is the length of the side of a regular hexagon and why?

Question

I think it is 1. Because from the Picture it Looks like that but can somebody explain me why this is so?

Answer 1

The hexacon can be partitioend into six equilateral triangles (three of them are shown in tge picture)

Answer 2

Consider a single triangle. By the argument of symmetry, the angle at the centre would be $2\pi/6$. Applying the law of cosines immediately tells you the length opposite the central angle. Let the length be $a$. $$a^2=1^2+1^2-2\cdot1\cdot1\cdot\cos(2\pi/6)\implies a=1$$