1. **State the problem:** Calculate the surface area of the given triangular prism. 2. **Identify the prism's parts:** The prism has two triangular bases and three rectangular faces. 3. **Calculate the area of one triangular base:** The triangle has base $b=5$ and height $h=10$, so area is $$\frac{1}{2} \times 5 \times 10 = 25.$$ This is the area of one triangular base. 4. **Calculate total area of two triangular bases:** Since there are two bases, total area for both is $$2 \times 25 = 50.$$ 5. **Calculate the area of the three rectangles:** - First rectangle has dimensions $20 \times 10$, area = $20 \times 10 = 200$. - Second rectangle has dimensions $20 \times 5$, area = $20 \times 5 = 100$. - Third rectangle corresponds to the side with the hypotenuse length $11.18$, so area = $20 \times 11.18 = 223.6$. 6. **Sum all the rectangular areas:** $$200 + 100 + 223.6 = 523.6.$$ 7. **Calculate total surface area:** Add the area of the two triangular bases and all rectangular areas: $$ 50 + 523.6 = 573.6.$$ **Final answer:** The surface area of the prism is $573.6$.