1. **State the problem:** We need to find the area of a circle given its diameter is 2 cm. 2. **Formula:** The area $A$ of a circle is given by the formula: $$A = \pi r^2$$ where $r$ is the radius of the circle. 3. **Find the radius:** The radius is half the diameter, so: $$r = \frac{d}{2} = \frac{2}{2} = 1 \text{ cm}$$ 4. **Calculate the area:** Substitute $r = 1$ cm into the area formula: $$A = \pi (1)^2 = \pi \text{ cm}^2$$ 5. **Final answer:** The area of the circle is $$\boxed{\pi \text{ cm}^2}$$