To find out how many square feet can be painted with 34 cans of paint, we can multiply the coverage of one can by the number of cans.
Each can covers 125 square feet, so:
\[ 34 \text{ cans} \times 125 \text{ square feet/can} = 4,250 \text{ square feet} \]
Therefore, the total area that can be painted with 34 cans is 4,250 square feet.