We have a 30'x30' covered run. We used bird netting. It is not foolproof, but it seems to be enough to make them think twice. We have had to repair hawk holes in the top....but they never managed to get in and kill any of the chickens.
Yes, hawks do go below the tree line. It seems like they prefer it, as opposed to the vultures who just fly over all of the areas. I have watched hawks swoop down under the tree line to try to catch my neighbors free range chickens. It was quite interesting to see how her flock reacted. Their alert calls sounded like air raid sirens for 10 minutes... til they felt it was all clear.