If the diameter of the coin is 2 centimeters, then the radius is 1 centimeter. Since the formula for the area of a circle is Area = πr^2, we can compute the area of the coin as follows:
Area = π x (1 cm)^2
= 3.14 cm^2
Since we rounded the radius to 1 centimeter, it is appropriate to round the area of the coin to the nearest hundredth. Therefore, the area of the coin is approximately 3.14 cm^2 or 3.14 square centimeters.