I decided to do some simple calculations of my own to check Musk's claim.
According to EIA, the per capita annual energy consumption in the US is 390 million BTU. That number is everything, from coal to nuclear, petroleum products, natural gas, biomass, hydro, wind, etc... In short, every source of energy that the US is currently consuming is in the above number.
Converting the above number from BTU to kWh, we use 90,600 kWh/year/person, or 250 kWh/day/person. Now, if you look at the TedTalk presented by MacKay, you will see the 250 kWh/day is what he shows on the chart at 5:24.
Now, the question becomes "How many solar panels do we need to generate 250 kWh/day?"
Of course, that is highly dependent on the weather, the season, the location, etc... But I will take my location here in the SW, which is the best location for solar panels in the US. And instead of using the daily requirement, I will use the annual requirement, assuming that we somehow can afford enough batteries or some form of energy storage to save energy from summer production to use in the winter.
According to nrel.gov, a 1 kW worth of PV panels at my location will produce 1800 kWh/year. For 90,600 kWh/year, we will need 50 kW worth of PV panels per person. Now, how large is this array of PV panels?
A high-efficiency panel of 61"x41" in production now can produce 350W. That's 17.4 sq.ft. for 350W, or 50 sq.ft. per kW. For 50 kW of panels, each person will need 2,500 sq.ft.
However, the number of 1800 kWh/year quoted by nrel.gov assumes that the panels are tilted up 30 deg at my location. The tilted panels then have to be spaced out to prevent partial shading. The ground area increases from 2,500 sq.ft. to 2900 sq.ft for each American.
The US population is 327 million. The total area for solar panels is then 948.3 billion sq.ft., or 34,015 sq.mi. That's a square of 184 mi x 184 mi. That's a bit larger than Musk's 100 mi x 100 mi square. It's not too far from what Midpack computes at 196 mi x 196 mi.
If we want to put the panels closer to the points of use to avoid the cost and losses of transmission lines, then we will need even more panels, because the above number is based on the best location in the US.
For example, in Portland, Oregon, a 1 kW of panels will have an annual production of 1180 kWh, instead of 1800 kWh. In Dayton, Ohio, it will be 1400 kWh/year.
PS. I made an error in computing the spacing of rows of panels to prevent shading. The sun angle in the winter is a lot lower than I thought, even here in the SW. However, I will not present the new number, because all we care here is just a rough order of magnitude.