how to derive the height of a hcp unit cell? please discuss in detail.

A,B,C,E (red dots) will represents the centres of sphere of atoms in HCP closed packing,

now, AB=BC=CA=EB = 2R (edge lengths of HCP)

  ,as BD divides the median through B in 2:1 ratio from B...

now EDB is rt. triangle,

by pythagores theorem :

=>

now, their will be another atom which will be mirror image of E on plane ABC

so, the height (c) of HCP will be 2h