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A square foot is a measure of surface area, and a mile is a measure of length. There are 5,280 feet in a mile and 27,878,400 square feet in a square mile.
Using the square milage you gave for Texas: 1 square mile = 5280 x 5280 square feet = 27,878,400 square feet. So 268,581 square miles = 7,487,608,550,400. For simplicity say 7.5 x 10^12. That divided by 7 x 10^9 is indeed over 1000 square feet per person.