Let's tweak this for a Primal diet. page

[llewin]

Family of 4?

http://1bog.org/files/2011/01/backyard_farm.jpg

[erikJ]

Drop the wheat and corn and learn to grow rotating crops and you would need an acre maybe less. If you did cow's instead of goats then you could cycle the cows in one pasture and then have the chickens come in and get the shorter grass and shoots, not to mention all those grubs and stuff. Plus if you do cows, neighbors could pool acreage and share bounty. If you built a large pond in there you could add ducks and geese that would help with slugs and the pond would help with a possible irrigation system. You could also add some bee hives in there too. And still on an acre.
You would need a family of four to do the work but I assume this family doesn't work or plan on having a truck or car. Cow driven buggy? Solar powered pick up would be nice.

[jfreaksho]

I've got in-laws who are big into sustainable agriculture and permaculture. I bet this estimate could be trimmed down greatly.

[Chaohinon]

Replace the grains with potatoes and/or sweet potatoes; they can yield up to 2-4 times more calories per acre than grains (and more protein, for that matter0. I'd also assume they take a little less work, but don't know that for sure.

Not sure if they can be used for animal feed, though.