Take two balls of string. Start in the center of the driveway, facing the arc of the curve. There are two borders of the driveway, each making a separate curve; the one farther away from you will be larger. Go to one end of the larger curve and unwind the string downward, past the smaller curve, until you are facing the driveway and are aligned with the approximate center of the arc. You will be in approximately the same position in which you started, only farther back. Leave the string and repeat on the other side. Keep unraveling the string until the two strings cross.
With a proctractor, measure the angle made by the string where it meets.
Caculate the fraction of a circle that your concave driveway makes by dividing the angle's degrees by 360. For example, if the angle formed is a 90 degree angle, you have 90/360, or 1/4 of a full circle.
Find the total area of this circle by measuring one of the lengths of string. This is your radius; square it and multiply the result by pi (3.14159) for the total area of your circle, multiplying that by the fraction you found in Step 3.
Find the radius that begins on the inner, rather than the outer, curve of your driveway and taking a piece of string to the same point. It should give you the same angle, but a different radius. Find the area of this circle by repeating Step 4.
Subtract the smaller area from the larger area. The remaining number is the area of your concave driveway.