There are only a couple obscure routing engines that can route through areas, so you will have to use interconnected linear ways probably.

What square are you mapping exactly?

If the entire square is open to cars, you should do something like the following:

On the square area itself set

place=square
area:highway=yes

Also connect all the other roads entering/exiting the square to each other, so that they are routable; make sure they all have appropriate highway=* tags set, so that routers don’t get confused.

Make sure that all pedestrian paths (sidewalks) are also connected together, using highway=crossing when appropriate.