1. **State the problem:** Find the volume of a triangular prism with a right triangle base where the base height is 5 cm, base length is 6 cm, and the prism length (depth) is 10 cm. 2. **Formula for volume of a triangular prism:** $$\text{Volume} = \text{Area of triangular base} \times \text{length of prism}$$ 3. **Formula for area of a triangle:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 4. **Calculate the area of the triangular base:** $$\text{Area} = \frac{1}{2} \times 6 \times 5 = \frac{1}{2} \times 30 = 15 \text{ cm}^2$$ 5. **Calculate the volume of the prism:** $$\text{Volume} = 15 \times 10 = 150 \text{ cm}^3$$ 6. **Final answer:** The volume of the triangular prism is **150 cm³**.