What is the boundary $ \partial ([a,b] \times [a,b])$ and how can I write it down mathematically rigorously?

What is the boundary of $ \partial ([a,b] \times [a,b])$?

I know that $ \partial ([a,b] \times [a,b])=\partial [a,b]^2=\overline{[a,b]^2}\setminus ([a,b]^2)^\circ=[a,b]^2\setminus (a,b)^2$

Visually the boundary $ \partial [a,b]$ is the edge of a rectangle with side lengths $a$ and $b$, but how can I write this down mathematically rigorously?

Idea:$ \partial ([a,b] \times [a,b])=\partial [a,b]^2=\overline{[a,b]^2}\setminus ([a,b]^2)^\circ=[a,b]^2\setminus (a,b)^2=\{[a,a+x]\cup [a+x,a]\cup [a+x,b]\cup [b,a+x]\, |\, x\in [0, b-a]\}$