1. The problem asks to find the area of a quarter circle with radius 6 cm. 2. The formula for the area of a full circle is $$A = \pi r^2$$ where $r$ is the radius. 3. Since we want the area of a quarter circle, we take one-fourth of the full circle's area: $$A_{quarter} = \frac{1}{4} \pi r^2$$. 4. Substitute $r = 6$ cm into the formula: $$A_{quarter} = \frac{1}{4} \pi (6)^2$$. 5. Calculate the square of the radius: $$6^2 = 36$$. 6. So, $$A_{quarter} = \frac{1}{4} \pi \times 36$$. 7. Simplify the fraction: $$A_{quarter} = 9\pi$$. 8. Using $\pi \approx 3.14$, calculate the numerical value: $$A_{quarter} \approx 9 \times 3.14 = 28.26$$ cm². 9. Therefore, the area of the quarter circle is approximately 28.26 cm².