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Wouldn't the panels be the same pitch as the roof, so you'd reduce the footprint there as well?

And if you have a hip roof, it may be an exercise in fitting a rectangular peg in a triangular hole.

https://www.infiniteenergy.com.au/wp-content/uploads/2016/06...

A pitched roof and installing on only half doesn't change it that much. If your roof is 45deg then you're talking about a 24x24 building. If that's two stories this is 1152sqft, still less than half the size of the median US house.

There are roof designs where even on a large house 21 panels won't fit, but looking around my neigborhood most houses could easily do that many.