1. **State the problem:** We need to find the volume of a right-angled triangular prism. The triangle face has sides 23 m and 38 m (hypotenuse), and the prism depth (length) is 11 m. 2. **Identify the formula:** The volume $V$ of a prism is given by: $$V = \text{Area of base} \times \text{length}$$ 3. **Find the area of the triangular base:** Since the triangle is right-angled, the two legs are perpendicular. One leg is 23 m, and the other leg is unknown. We know the hypotenuse is 38 m. 4. **Calculate the other leg using Pythagoras theorem:** $$\text{other leg} = \sqrt{38^2 - 23^2} = \sqrt{1444 - 529} = \sqrt{915}$$ 5. **Simplify the square root:** $$\sqrt{915} \approx 30.25$$ 6. **Calculate the area of the triangle:** $$\text{Area} = \frac{1}{2} \times 23 \times 30.25 = \frac{1}{2} \times 696.25 = 348.125$$ 7. **Calculate the volume of the prism:** $$V = 348.125 \times 11 = 3829.375$$ 8. **Round to 1 decimal place:** $$V \approx 3829.4$$ 9. **Include units:** The volume is in cubic meters. **Final answer:** $$\boxed{3829.4\ \text{m}^3}$$