if you want to ‘cover’ all at once with a single poly use “Polycap” . ( but judging from the pic i doubt if thats what you want since the poly will be not coplanar . )
if you want to ‘draw’ polys following your mesh flow , id suggest to use “Polyknit” . once you call that , start selecting points over the mesh and finally , press enter . do some tentatives first in order to understand how it wants the points ‘served’ .. there is visual feedback too .
except the things that cannot be seen , nothing is like it seems .