1. **Stating the problem:** Find the area of the shaded rectangular face of the 3D prism with dimensions 9 m, 5 m, and 7 m. 2. **Identify the shaded face dimensions:** The shaded face is a rectangle on one side of the prism. Since the prism has dimensions 9 m (length), 5 m (height), and 7 m (height), the shaded face must be one of the rectangular sides. 3. **Determine which dimensions form the shaded rectangle:** Assuming the shaded face is the side with dimensions 9 m and 5 m (top length and right height). 4. **Formula for area of a rectangle:** $$\text{Area} = \text{length} \times \text{width}$$ 5. **Calculate the area:** $$\text{Area} = 9 \times 5 = 45$$ 6. **Answer for the first problem:** The area of the shaded part is $45$ square meters. --- 7. **Second problem:** Find the distance if a man walks around thrice the figure with dimensions 1 km and 14 dm. 8. **Convert units to the same unit:** 1 km = 1000 m 14 dm = 1.4 m 9. **Calculate the perimeter of the rectangle:** $$P = 2 \times (\text{length} + \text{width}) = 2 \times (1000 + 1.4) = 2 \times 1001.4 = 2002.8$$ meters 10. **Distance walked thrice around:** $$3 \times 2002.8 = 6008.4$$ meters 11. **Answer for the second problem:** The man walks $6008.4$ meters around the figure thrice. **Final answers:** - Area of shaded part: $45$ m$^2$ - Distance walked thrice: $6008.4$ m