1. **State the problem:** We need to find the volume and surface area of a triangular prism with sides of the triangular base $s_1=3.75$, $s_2=5.5$, $s_3=2.25$, length $L=22$, and height $h=10.2$ (height of the triangle). 2. **Formula for volume of a triangular prism:** $$\text{Volume} = \text{Area of triangular base} \times \text{length}$$ 3. **Formula for area of a triangle:** Since we have the height $h=10.2$ of the triangle, the area is: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ We can choose $s_2=5.5$ as the base. 4. **Calculate the area of the triangular base:** $$\text{Area} = \frac{1}{2} \times 5.5 \times 10.2 = \frac{1}{2} \times 56.1 = 28.05$$ 5. **Calculate the volume:** $$\text{Volume} = 28.05 \times 22 = 617.1$$ 6. **Formula for surface area of a triangular prism:** $$\text{Surface Area} = 2 \times \text{Area of triangular base} + \text{Perimeter of base} \times \text{length}$$ 7. **Calculate the perimeter of the triangular base:** $$\text{Perimeter} = s_1 + s_2 + s_3 = 3.75 + 5.5 + 2.25 = 11.5$$ 8. **Calculate the surface area:** $$\text{Surface Area} = 2 \times 28.05 + 11.5 \times 22 = 56.1 + 253 = 309.1$$ **Final answers:** - Volume = $617.1$ cubic units - Surface Area = $309.1$ square units