1. **State the problem:** Find the volume of a triangular prism with a right triangle base having legs of 5 cm and 2 cm, and a prism length of 8 cm. 2. **Formula:** The volume $V$ of a triangular prism is given by: $$V = \text{Area of triangular base} \times \text{length of prism}$$ 3. **Calculate the area of the triangular base:** The base is a right triangle, so its area $A$ is: $$A = \frac{1}{2} \times \text{leg}_1 \times \text{leg}_2 = \frac{1}{2} \times 5 \times 2$$ 4. **Simplify the area:** $$A = \frac{1}{2} \times 10 = 5 \text{ cm}^2$$ 5. **Calculate the volume:** $$V = A \times \text{length} = 5 \times 8 = 40 \text{ cm}^3$$ 6. **Final answer:** The volume of the prism is $40$ cubic centimeters, rounded to the nearest tenth it remains $40.0$ cm³.