1. **State the problem:** Find the surface area of a rectangular prism with dimensions 7 cm (height), 3 cm (width), and 1 cm (depth). 2. **Formula:** The surface area $S$ of a rectangular prism is given by: $$S = 2(lw + lh + wh)$$ where $l$, $w$, and $h$ are the length, width, and height. 3. **Assign values:** Here, $l = 7$, $w = 3$, and $h = 1$. 4. **Calculate each product:** $$lw = 7 \times 3 = 21$$ $$lh = 7 \times 1 = 7$$ $$wh = 3 \times 1 = 3$$ 5. **Sum the products:** $$21 + 7 + 3 = 31$$ 6. **Multiply by 2:** $$S = 2 \times 31 = 62$$ 7. **Final answer:** The surface area of the rectangular prism is $62$ square centimeters.