How Do I Calculate Square Feet In An Area That Has Multiple Curves And Corners?

Well the best bet you would have is to put grid squares of 1ft on you drive way and count out how many full squares you have how many half squares and how many quarter squares. This is by far the easiest method.
if you want greater accuracy then use smaller squares like 1/2ft or 1/4ft.

its rough and crude but it does the job well. Other than that the only other way i can think of is by construction a f(x) curve for your driveway and integrating the formula between 0 and the width of your driveway.

hope this helped