1. **State the problem:** Find the surface area of a rectangular prism with dimensions length $= 12$ cm, width $= 15$ cm, and height $= 3$ cm. 2. **Formula for surface area of a rectangular prism:** $$SA = 2(lw + lh + wh)$$ where $l$ is length, $w$ is width, and $h$ is height. 3. **Calculate the area of the top and bottom:** Top and bottom are rectangles with dimensions length and width. $$\text{Area}_{top+bottom} = 2 \times (l \times w) = 2 \times (12 \times 15) = 2 \times 180 = 360$$ 4. **Calculate the area of the front and back:** Front and back are rectangles with dimensions length and height. $$\text{Area}_{front+back} = 2 \times (l \times h) = 2 \times (12 \times 3) = 2 \times 36 = 72$$ 5. **Calculate the area of the sides:** Sides are rectangles with dimensions width and height. $$\text{Area}_{sides} = 2 \times (w \times h) = 2 \times (15 \times 3) = 2 \times 45 = 90$$ 6. **Calculate total surface area:** $$SA = 360 + 72 + 90 = 522$$ **Final answer:** The total surface area of the rectangular prism is **522 cm\textsuperscript{2}**.