1. The problem asks for the area of a quarter circle with radius $4$ units. 2. The area of a full circle is given by the formula $$A=\pi r^2$$ where $r$ is the radius. 3. Since we have a quarter circle, its area is one-fourth of the full circle's area. 4. Substitute the radius $r=4$ into the formula for the full circle area: $$A_{full} = \pi \times 4^2 = 16\pi$$ 5. Now find the quarter circle area: $$A_{quarter} = \frac{1}{4} \times 16\pi = 4\pi$$ 6. If we use the approximate value $\pi \approx 3.14$, then $$A_{quarter} \approx 4 \times 3.14 = 12.56$$ 7. So the area of the quarter circle is exactly $$4\pi$$ units squared or approximately $12.56$ units squared.