1. **Problem Statement:** Calculate the surface area 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 surface area $S$ of a right triangular prism is given by: $$S = ext{Lateral surface area} + 2 \times \text{Area of triangular base}$$ where the lateral surface area is the perimeter of the triangular base times the length of the prism. 3. **Calculate the hypotenuse of the triangular base:** Using the Pythagorean theorem: $$\text{hypotenuse} = \sqrt{1.7^2 + 2^2} = \sqrt{2.89 + 4} = \sqrt{6.89} \approx 2.625$$ 4. **Calculate the perimeter of the triangular base:** $$P = 1.7 + 2 + 2.625 = 6.325$$ 5. **Calculate the lateral surface area:** $$\text{Lateral surface area} = P \times \text{length} = 6.325 \times 4 = 25.3$$ 6. **Calculate the area of the triangular base:** $$A = \frac{1}{2} \times 1.7 \times 2 = 1.7$$ 7. **Calculate the total surface area:** $$S = 25.3 + 2 \times 1.7 = 25.3 + 3.4 = 28.7$$ 8. **Answer:** The surface area of the right triangular prism is **28.7 square feet**.