I guess that this is folding a piece of paper for example. Then you have:
Set up equations now and this should be easy.
EDIT: Did you get your equations?
(a) Show that
(b) Find the domain of C.
(c) Determine the x-value that minimizes C.
(d) Determine the minimum length of C.
I am unsure on how to approach this problem.... it would seem that I would need more angle information. It seems I could solve the left region of the polygon, but I have no idea what to do with the right-hand portion.