1. **State the problem:** We need to find the total surface area of a building that is 8m tall, with a floor plan shaped like a large rectangle with a smaller rectangular cutout at the bottom-left corner. The surface area includes all walls and the roof. 2. **Identify dimensions:** The outer rectangle has dimensions 27cm by 22cm, and the inner cutout rectangle has dimensions 10cm by 18cm. The building height is 8m. 3. **Convert all lengths to meters:** - Outer rectangle: 27cm = 0.27m, 22cm = 0.22m - Inner cutout: 10cm = 0.10m, 18cm = 0.18m 4. **Calculate the floor area:** - Area of outer rectangle: $$0.27 \times 0.22 = 0.0594\,m^2$$ - Area of cutout rectangle: $$0.10 \times 0.18 = 0.018\,m^2$$ - Floor area (outer minus cutout): $$0.0594 - 0.018 = 0.0414\,m^2$$ 5. **Calculate the roof area:** The roof covers the same area as the floor, so roof area = $$0.0414\,m^2$$ 6. **Calculate the perimeter of the floor plan:** - The perimeter includes the outer rectangle minus the cutout plus the inner cutout edges. - Outer rectangle perimeter: $$2(0.27 + 0.22) = 0.98\,m$$ - The cutout creates an inner perimeter of $$2(0.10 + 0.18) = 0.56\,m$$ - Total perimeter for walls = outer perimeter + inner cutout perimeter = $$0.98 + 0.56 = 1.54\,m$$ 7. **Calculate the wall surface area:** - Wall area = perimeter $\times$ height = $$1.54 \times 8 = 12.32\,m^2$$ 8. **Calculate total surface area:** - Total surface area = wall area + roof area = $$12.32 + 0.0414 = 12.3614\,m^2$$ **Final answer:** The total surface area of the building, including the roof, is approximately $$12.36\,m^2$$.