1. **State the problem:** We have a larger square with side length 18 cm and a smaller square carpet inside it with side length 9 cm. The carpet is centered, and there is a 1 cm margin on the right side. 2. **Understand the problem:** The unshaded region is the area of the larger square minus the area of the carpet. 3. **Formula for area of a square:** $$\text{Area} = \text{side}^2$$ 4. **Calculate the area of the larger square:** $$18^2 = 324 \text{ cm}^2$$ 5. **Calculate the area of the carpet (smaller square):** $$9^2 = 81 \text{ cm}^2$$ 6. **Calculate the area of the unshaded region:** $$324 - 81 = 243 \text{ cm}^2$$ 7. **Conclusion:** The area of the unshaded region (the border around the carpet) is $243$ cm$^2$.