For my project, I'm growing Baker's yeast and probiotics in two liquid cultures before mixing them together and plating them. I'm trying to measure the impact of the probiotics on the yeast. How could I measure the amount of fungi on the plate, whether by cell counting or surface area?
You can count the individual colonies on the plate, with this number being the number of "Colony Forming Units" (CFU), as theoretically, only a single cell is needed to spawn a colony.
To do this though, you will need to do a serial dilution of your liquid cultures before plating, so you would have one plate of 10$^0$ dilution, then 10$^1$, 10$^2$, and so on, generally a ten-fold dilution is performed.
Hopefully this will yield at least one plate with a countable number of colonies, that is - not too many, and not too few - usually 30-300.
cfu/ml = (no. of colonies x dilution factor) / volume of culture plated
This usually yields a very large number, so it is common to then take the log of this number, and report that as your result.
And then you will be able to compare your results between probiotics. It's a very good idea to do replicates of each dilution!
As explained by user GrumpyMammoth, you can do serial dilutions until the colonies are few enough to be counted and then calculate the CFUs using the dilution factor.
If you do not want to count the colonies yourself, you can use ImageJ's "Analyze particles" function. This will give you the number of colonies.
ImageJ's "Analyze particles" function will also give you the colony size (surface area) in pixels. This can be converted into millimeters in ImageJ by opening the Image>Properties tab and changing the pixel width parameter.