1. **State the problem:** Find the surface area of the L-shaped solid composed of two rectangular prisms joined together. 2. **Identify dimensions:** - Larger prism: length = 18 cm, width = 7 cm, height = 5 cm - Smaller prism: length = 5 cm, width = 5 cm, height = 5 cm 3. **Formula for surface area of a rectangular prism:** $$SA = 2(lw + lh + wh)$$ where $l$ = length, $w$ = width, $h$ = height. 4. **Calculate surface area of larger prism:** $$SA_1 = 2(18 \times 7 + 18 \times 5 + 7 \times 5)$$ $$= 2(126 + 90 + 35) = 2(251) = 502 \text{ cm}^2$$ 5. **Calculate surface area of smaller prism:** $$SA_2 = 2(5 \times 5 + 5 \times 5 + 5 \times 5)$$ $$= 2(25 + 25 + 25) = 2(75) = 150 \text{ cm}^2$$ 6. **Calculate the area of the overlapping face:** The smaller prism is attached on top of the larger prism with a face of $5 \times 5$ cm. $$A_{overlap} = 5 \times 5 = 25 \text{ cm}^2$$ 7. **Calculate total surface area of the L-shaped solid:** Since the overlapping face is counted twice in the sum of individual surface areas, subtract it once: $$SA_{total} = SA_1 + SA_2 - 2 \times A_{overlap}$$ $$= 502 + 150 - 2 \times 25 = 652 - 50 = 602 \text{ cm}^2$$ 8. **Final answer:** The surface area of the L-shaped solid is **602 cm²**.