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Your problem with the math there is that a square foot is 12x12 = 144, not 12+12 = 24. So you can actually only fit 6 or so chicks in there at 1sq ft each.
My brooder was 2' high plywood nailed in a box to be 4'x4'. I have 24 chicks in there at nearly 4 weeks... and they need more room now, so thankfully they're going into their coop this weekend. But it worked well for the first 2-3 weeks, and really it's not that bad right now. It's not like they're fighting, there's no smells or anything, but they just look like need more room to run and play. Oh also, at 2' high, they were roosting on the edges of the brooder by the end of 2 weeks, so you'd need a lid (or smart chicks with good balance who know to stay on the inside!)