1. **State the problem:** We need to find the volume of a right triangular prism with a triangular base having side lengths 2 in, 4 in, and 5 in, and a height (length) of the prism of 3 in. 2. **Formula for volume of a prism:** $$\text{Volume} = \text{Area of base} \times \text{height}$$ 3. **Find the area of the triangular base:** The base is a right triangle (right angle indicated). The legs are 2 in and 4 in (the sides forming the right angle). Area of right triangle = $$\frac{1}{2} \times \text{leg}_1 \times \text{leg}_2 = \frac{1}{2} \times 2 \times 4$$ 4. Calculate the area: $$\frac{1}{2} \times 2 \times 4 = \frac{\cancel{2}}{1} \times \cancel{2} \times 4 = 4$$ square inches 5. **Calculate the volume:** $$\text{Volume} = \text{Area of base} \times \text{height} = 4 \times 3 = 12$$ cubic inches **Final answer:** The volume of the prism is $12$ cubic inches.