1. **State the problem:** We need to find the area of a compound shape made of a rectangle and a sector of a circle. 2. **Identify given values:** - Rectangle length = 14 cm - Rectangle height = 8 cm - Sector radius = 8 cm (same as rectangle height) - Sector central angle = 41° 3. **Formula for area of rectangle:** $$\text{Area}_{rectangle} = \text{length} \times \text{height}$$ 4. **Formula for area of sector:** $$\text{Area}_{sector} = \frac{\theta}{360} \times \pi r^2$$ where $\theta$ is the central angle in degrees and $r$ is the radius. 5. **Calculate area of rectangle:** $$\text{Area}_{rectangle} = 14 \times 8 = 112 \text{ cm}^2$$ 6. **Calculate area of sector:** $$\text{Area}_{sector} = \frac{41}{360} \times \pi \times 8^2 = \frac{41}{360} \times \pi \times 64$$ 7. **Simplify sector area:** $$\text{Area}_{sector} = \frac{41}{360} \times 64 \pi = \frac{41 \times 64}{360} \pi = \frac{2624}{360} \pi$$ 8. **Calculate numerical value:** $$\text{Area}_{sector} \approx \frac{2624}{360} \times 3.1416 \approx 7.2889 \times 3.1416 \approx 22.9 \text{ cm}^2$$ 9. **Calculate total area:** $$\text{Area}_{total} = \text{Area}_{rectangle} + \text{Area}_{sector} = 112 + 22.9 = 134.9 \text{ cm}^2$$ 10. **Final answer rounded to 1 decimal place:** $$\boxed{134.9 \text{ cm}^2}$$