All the strive in the world got me to thinking...One of those hmm moments Okay...There's 7 billion people on the planet and I started with the surface area of the earth. Then I backed out oceans, sea, lakes, mountains and deserts. Everywhere humans can not live and came up with 1.55 X 108 square feet of living space. So that divided by 7 billion gives each person ~ 450 square feet of living space. I've doubled checked it and can't believe my answer. There's more frigging room in a 2-car garage. Let me google it to check... Nope! The google answer gives ~ 5 acres but doesn't back out uninhabitable land. Humans can't live there so I disagree with the 5 acre number and don't believe my own answer. Crap! I'm no Einstein but something's gotta give. Makes me think of George Carlin, "The planet will shake us off like a bad case of fleas." Oh Well, now that I've brightened your day, think I'll have a glass of wine and go play with the dog.
I am reminded of the book, "Miles from Nowhere", by Barbara Savage. It's an account of her and her husband's trip riding their bikes around the world. One thing they noted was, in much of the world there were few places not occupied by people. So where one can ride hundreds and hundreds of miles across the US and not see anyone, when for example, they rode across some remote land outside of Morocco, there would always be people there. Populations are self limiting. When we run out of food, water and air, the population will thin itself.
Your square footage for the living space is way off. Are you sure you calculated the surface area of the earth correctly? By the way, I did a quick search, and one website got 2.3 acres per person.
Like Khan, you are unaccustomed to thinking in three dimensions. Also, people do live in mountains and in desert areas. However, resources are a real issue. All life depends, at some level, on solar energy converted to chemical energy through photosynthesis, releasing oxygen at the same time. Most land-dwelling life also depends on fresh water (also a solar-energy-driven process, rate-dependent on surface area normal to the line connecting the sun to the point on the Earth's surface. Like other animals, the closer you pack humans together, the faster they will break into lethal combat.
Particularly since we are not natural herd or hive animals. Humans are designed to run in packs. For the VAST majority of our evolutionary history we lived in groups of around twenty.