If you click on a surface SolidWorks Simulation will give you the contact force (resultant and components). Just right click on the results folder and choose list result forces). If you create a stress plot you can choose to plot contact pressure, which will give you an idea of contact are.
Estimating it is quite tricky: here's a post from my blog that shows how: http://solidworkseducation.blogspot.it/2012/04/determinazione-dellarea-di-contatto-tra.html?m=1
- You can get the force, assuming no other contacts exist on the selected surface by the method suggested above by Alessandro.
- You could infer the areas you are interested in by getting the peak deflection of the sphere (ie its center or initial point of contact) and assume the contact patch is spherical (likely a very close approximation if the sphere is much stiffer than the rubber) and the just truncate the sphere at the required displacement, assuming initial tangency contact. You can force a node at the initial contact point via a split line.