Why calculate the aperture width?
For exposure, only the f-stop matters.

If you used the results of, say, 40/8 = 5 to set your exposure, i.e. chose a shutterspeed to match 5, you would indeed be more than 1 stop (1.36 in fact) stop off (underexposed) from what it should be.

If you set the lens to f/8, use the shutterspeed to match f/8. Nothing else.