I measure the square feet of the lawn area. I use this a starting number for the price of the lawn. I then make adjustments for trimming, blowing, etc. As for amount per square foot you are going to get a wide variety depending upon the area. You might only be able to get $2 a square foot and someone else in another area could get $4 for the same property.
In my opinion, pricing by area can work well IF the price per 1000 sq ft includes all your job costs, fixed costs, and time adjustments for the individual property. These are items you have to work out for your operation over time using actual data (total hours use of the mower and handheld equipment, gasoline consumption, maintenance & repair costs, insurance, replacement of the mower and other equipment, vehicle costs, off site hours for sharpening blades, invoicing, advertising, phone, office expenses, CPA, Etc). There is alot of detail and analysis that goes into developing an accurate price, the first of which is to determine how long it takes to mow a known open area with your equipment. Once you know that, depending upon your need per hour, you modify those times based upon the additional time it will take for a specific property. It takes some work and record keeping but it is worth the effort in the long run for me because I know I recover my operating costs, fixed overhead plus profit. For instance, I don't have a certain price for one acre. A flat open acre lot with little trimming, blowing or edging will be less than a wooded acre with a long drive, sidewalk and curb. I've had folks stop while I'm loading up and ask "how much to mow my yard" like there is a fixed price. I tell them I have to take a look. Some people just drop it right there, which is fine with me. There is no 'flat rate book' like the auto mechanics use.