The contact area as you have drawn is it zero. For example, the area where a plane touches a sphere? ZERO. A single point of contact has ZERO area. Even if the circlular region is actually intended to be a circular rod, the area of the contact where a plane touches a cylinder is again at most a line, which again has area ZERO. Zero area. Nil. Zip. Nada. Zilch.
In general, the area of contact between almost any such hard surfaces, will be at most a line, unless you have planar regions that are in full contact. Again, zero except for the rare case, and you have not drawn this as one of those rare cases. So the area of contact is zero.
If the surfaces are soft, so you have some surface deformation based on a force exerted, then yes, you have a non-zero contact area. But that would require some far more sophisticated modling, of the deformations of the objects. Now at the very least we are talking finite element modeling to determine the deformations of those solid bodies, to then determine how a singe point of contact expands into a region of contact. (At some point in the past, people were probably writing theses on something like this. If the objects are sufficiently internally complex, there is still probably a thesis waiting to be written.)
If you are willing to assume some fixed amount of deformation, then you could probably make some simple assumptions. Start with the line or point of contact, then decide how far out the deformations would be seen, and then turn the line or point into a rough polygonal region. Contact the area from that. But unless you have information about the stiffness of the objects in contact, or some understanding about how they would deform, AND you know the forces involved to know the extent of deformation, there is little to be done.
