1. **State the problem:** Find the volume of a right triangular prism with a base triangle having legs 10 cm and 4 cm, and a prism depth of 2 cm. 2. **Formula:** The volume $V$ of a prism is given by $$V = \text{Base Area} \times \text{Height (depth)}$$ 3. **Calculate the base area:** The base is a right triangle, so its area is $$\text{Base Area} = \frac{1}{2} \times \text{leg}_1 \times \text{leg}_2 = \frac{1}{2} \times 10 \times 4$$ 4. **Simplify the base area:** $$\frac{1}{2} \times 10 \times 4 = \frac{1}{2} \times 40 = 20$$ 5. **Calculate the volume:** Multiply the base area by the prism depth: $$V = 20 \times 2 = 40$$ 6. **Final answer:** The volume of the prism is $40$ cubic centimeters.