Question

what is the length of any diagonal of a regular pentagon with a side of 20mm?

Answer 1

The ratio of the diagonal to a side is the "golden" ratio, (1+sqrt5)/2 or appx 1.618 For a complicated proof of this see http://whistleralley.com/polyhedra/pentagon.htm

but you can work it out for yourself much simpler than that. Work through his analysis.