1. **State the problem:** We need to find the volume and surface area of a triangular prism with side lengths 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 here is ambiguous but we assume it is the height of the triangular base). 2. **Formula for volume of a prism:** $$\text{Volume} = \text{Base Area} \times \text{Length}$$ 3. **Calculate the area of the triangular base:** Use Heron's formula for the area of a triangle with sides $a$, $b$, and $c$: $$s = \frac{a+b+c}{2}$$ $$\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}$$ 4. **Calculate semi-perimeter:** $$s = \frac{3.75 + 5.5 + 2.25}{2} = \frac{11.5}{2} = 5.75$$ 5. **Calculate area:** $$\text{Area} = \sqrt{5.75(5.75-3.75)(5.75-5.5)(5.75-2.25)} = \sqrt{5.75 \times 2 \times 0.25 \times 3.5}$$ $$= \sqrt{5.75 \times 2 \times 0.25 \times 3.5} = \sqrt{10.0625} \approx 3.17$$ 6. **Calculate volume:** $$\text{Volume} = 3.17 \times 22 = 69.74$$ 7. **Calculate surface area:** Surface area = 2 × base area + perimeter × length 8. **Calculate perimeter:** $$P = 3.75 + 5.5 + 2.25 = 11.5$$ 9. **Calculate surface area:** $$\text{Surface Area} = 2 \times 3.17 + 11.5 \times 10.2 = 6.34 + 117.3 = 123.64$$ **Final answers:** - Volume $\approx 69.74$ cubic units - Surface area $\approx 123.64$ square units