1. **State the problem:** Calculate the total surface area of a figure composed of a square base with side length 20 cm and four identical triangles attached to each side. Each triangle has a base of 20 cm and a height of 9 cm. 2. **Formula used:** - Area of square: $$A_{square} = s^2$$ where $s$ is the side length. - Area of triangle: $$A_{triangle} = \frac{1}{2} \times base \times height$$ - Total surface area: $$A_{total} = A_{square} + 4 \times A_{triangle}$$ 3. **Calculate the area of the square:** $$A_{square} = 20^2 = 400$$ cm$^2$ 4. **Calculate the area of one triangle:** $$A_{triangle} = \frac{1}{2} \times 20 \times 9 = \frac{1}{2} \times 180 = 90$$ cm$^2$ 5. **Calculate the total area of the four triangles:** $$4 \times 90 = 360$$ cm$^2$ 6. **Calculate the total surface area:** $$A_{total} = 400 + 360 = 760$$ cm$^2$ **Final answer:** The total surface area is **760 cm$^2$**.