1. The problem asks for the area of a quarter circle with radius 2 units. 2. The formula for the area of a full circle is $$A = \pi r^2$$ where $r$ is the radius. 3. Since this is a quarter circle, the area is one-fourth of the full circle's area: $$A_{quarter} = \frac{1}{4} \pi r^2$$ 4. Substitute $r = 2$: $$A_{quarter} = \frac{1}{4} \pi (2)^2 = \frac{1}{4} \pi \times 4 = \pi$$ 5. Using $\pi \approx 3.14$, the decimal area is: $$A_{quarter} \approx 3.14$$ 6. Therefore, the area of the quarter circle is exactly $\pi$ units² or approximately 3.14 units².