1. **Problem Statement:** Find the area of a quarter circle with radius $2$ units. 2. **Formula:** The area $A$ of a full circle is given by $$A = \pi r^2$$ where $r$ is the radius. 3. **Important Rule:** A quarter circle is one-fourth of a full circle, so its area is $$\frac{1}{4} \pi r^2$$. 4. **Calculation:** Substitute $r = 2$ into the formula: $$A = \frac{1}{4} \pi (2)^2 = \frac{1}{4} \pi \times 4 = \pi$$ 5. **Answer:** The exact area of the quarter circle is $$\pi$$ units². 6. **Decimal Approximation:** Using $\pi \approx 3.14$, the area is approximately $$3.14$$ units².