I'm not sure I understood, your 3T/m² floor and your 9T posts, so I'd say 3m² of surface area for your plate ; ), because 3x3 = 9 (+ a koef of security adapted to this application). But this seems too simple to me, shouldn't you take into account the height of your pole and the possible buckling under load? Its environment?. And of course, put gussets to better distribute the load.
Indeed in theory it would need a 3m² support. But it remains in the case where the plate is non-deformable, of negligible mass, and perfectly flat (the ground also by the way). In practice, this is far from being the case...
GT22 is right about an essential security coeff!
The part you enclose is 1m40x1m40 ep30mm (weight 500kg)
I understand that my plate must have a surface of 3m² that's for sure. But in my case I need to know the thickness. Is there a rule for defining a load distribution plate?