Here's an answer that goes in and out of figuration, becoming more figurative than literal and then more literal than figurative, stimulated by the hint.
The answer we arrrive at is that
the field is ancient Rome, or anywhere else that people have used Roman numerals.
The working is as follows.
We want $\pi^2$, i.e.
the result of taking $\pi$, the ratio between the circumference and diameter of a circle, and getting it to operate on itself to give us a square. Alternatively, to square something is to make a square out of it.
let's get figurative. How do we make a square out of the usual figure for $\pi$? Easy. Start by making a copy and turning it round:
stick the rotated copy onto the bottom:
now made a square. It's got bits sticking out of it (outside of the box), but we've still made a square by getting $\pi$ to operate on itself. So we've squared $\pi$.
Go back to being literal. What have we got? The Roman numeral for the number 2. So we've squared $\pi$ and got 2.
I realise the usage of literal here is questionable. Another weakness is that the meaning of $\pi$, which the setter stresses, doesn't get a look-in. Nonetheless, the train of thought goes from meaning to figure to figure to meaning, which fits nicely with the hint and works as a way of getting $\pi^2$ to equal 2.