I don't know of any easy way to measure the contact area. I can think of a couple of work-arounds that might work. If the contact is planar, then you could put a sketch on a plane parallel to the contact. Convert Entities on the edges of the two parts that contact. Trim the edges to get the contact patches. Use the Measure tool to measure the area of the patches.
If the contact isn't planar, you might try modifying your mate to progressively increase the interference between the parts, using the Interference tool to measure the volume of the interference. The volume divided by the interference will give you an approximate area. Plotting the change of area as the interference approaches zero should give you a better estimate of the area.