1. **State the problem:** We have a rectangular paperboard measuring 27 inches long and 22 inches wide. A semicircle with diameter equal to the width (22 inches) is cut out from the rectangle. We need to find the area of the remaining paperboard. 2. **Formula for area of rectangle:** $$\text{Area}_{rectangle} = \text{length} \times \text{width}$$ 3. **Formula for area of semicircle:** $$\text{Area}_{semicircle} = \frac{1}{2} \pi r^2$$ where $r$ is the radius of the semicircle. 4. **Calculate the area of the rectangle:** $$27 \times 22 = 594 \text{ in}^2$$ 5. **Calculate the radius of the semicircle:** $$r = \frac{22}{2} = 11 \text{ in}$$ 6. **Calculate the area of the semicircle:** $$\frac{1}{2} \times 3.14 \times 11^2 = \frac{1}{2} \times 3.14 \times 121 = \frac{1}{2} \times 379.94 = 189.97 \text{ in}^2$$ 7. **Calculate the remaining area:** $$594 - 189.97 = 404.03 \text{ in}^2$$ **Final answer:** The area of the paperboard that remains is **404.03 in²**.