1. **Problem Statement:** Calculate the volume of a right triangular prism with legs of the right triangle base measuring $1.7$ feet and $2$ feet, and the prism length is $4$ feet. 2. **Formula:** The volume $V$ of a right triangular prism is given by: $$V = \text{Area of triangular base} \times \text{length of prism}$$ 3. **Calculate the area of the triangular base:** Since the triangle is right-angled, the area $A$ is: $$A = \frac{1}{2} \times \text{leg}_1 \times \text{leg}_2 = \frac{1}{2} \times 1.7 \times 2$$ 4. **Calculate the area:** $$A = \frac{1}{2} \times 3.4 = 1.7$$ square feet 5. **Calculate the volume:** $$V = A \times \text{length} = 1.7 \times 4 = 6.8$$ cubic feet 6. **Answer:** The volume of the right triangular prism is **6.8 cubic feet**.