It’s very common to use km^2 (or m^2 or whatever) as a unit of area, with the understanding that a square with x km sides has area x^2 km^2.
I can see what you’re saying, but I think most people would call that area ‘over 145 000 square km’ or something, rather than talk about the side length.
Square x and x squared is the same thing. The proper way to say this is “A square of 381 km width”
It’s very common to use km^2 (or m^2 or whatever) as a unit of area, with the understanding that a square with x km sides has area x^2 km^2. I can see what you’re saying, but I think most people would call that area ‘over 145 000 square km’ or something, rather than talk about the side length.