1. **State the problem:** We need to find the diameter of a circular rug given its circumference is 12.56 yards. 2. **Formula used:** The circumference $C$ of a circle is related to its diameter $d$ by the formula: $$C = \pi d$$ 3. **Rearrange the formula to solve for diameter:** $$d = \frac{C}{\pi}$$ 4. **Substitute the given circumference:** $$d = \frac{12.56}{\pi}$$ 5. **Calculate the diameter:** Using $\pi \approx 3.1416$, $$d = \frac{12.56}{3.1416}$$ 6. **Simplify the fraction:** $$d = \cancel{\frac{12.56}{3.1416}} = 4.00$$ 7. **Final answer:** The diameter of the rug is approximately **4.00 yards**.