1. **State the problem:** We need to find the area of a circular stained-glass window with a diameter of 4 yards. 2. **Formula for the area of a circle:** 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: $$r = \frac{4}{2} = 2 \text{ yards}$$ 4. **Calculate the area:** Substitute $r=2$ into the area formula: $$A = \pi (2)^2 = \pi \times 4 = 4\pi$$ 5. **Approximate the area:** Using $\pi \approx 3.1416$, $$A \approx 4 \times 3.1416 = 12.5664$$ 6. **Round the answer:** Rounded to the nearest hundredth, $$A \approx 12.57 \text{ square yards}$$ **Final answer:** The area of the window is approximately $12.57$ square yards.