EFFECTIVE WIDTH OF EXISTING SLAB

I would use 35 deg (to horizontal) angle from each base plate corner like you drew. IF the slab is reinforced then you could see if it would span further thus allowing for larger width/length to be considered effective. Same could be said for unreinforced slab. You could also check how far it could span, under a point load. Looks like you have about 8" thick slab which is a decent thickness to carry some concentrated loads. However if it were me I'd make them cut it out and pour a foundation below the column. Unless I put in a lightly loaded post, I never like them just on slab. Not sure what load you have but looks like a decent size column from your drawing with a large load.

It's going to vary with the flexibility of the slab and the soil underneath. (The magnitude will vary as well.) But it shouldn't be any less than the effective width you drew. (I.e. a 30-45 degree angle from the column edge.)

Unless the load is light, I'd put a 12" thick footing under it...

Dik