The square of any measurement unit for length (square meter, square foot etc.) will be used to measure surfaces of areas. Just by looking in one direction you will not cover a surface.
To do that U have to look all around your current position. This way your sight will cover the area comprised between your fixed position and the most distant still clearly visible terrain located 12 miles all around -- thus outlining a out-most still visible circle.
So what shape is the surface inside a circle -- a disk.
And which formula gives a disc's area -- π×(radius)2 = 3.1416 × 122 = 3.1416 × 144 etc.