1. Stating the problem: We need to verify by calculation that the area of a rectangular cardboard sheet is 1600 cm^2 given its dimensions: Height = 10 cm, Base = 10 cm, Length = 20 cm, and that it has a square base. 2. Understanding the shape: Since the base is square, its areas of the base will be $10 \text{ cm} \times 10 \text{ cm} = 100 \text{ cm}^2$. 3. Calculate the surface area of the rectangular box (net): The total surface area consists of: - The base (square) area: $100 \text{ cm}^2$ - The top (also square): $100 \text{ cm}^2$ - The sides: there are 4 sides Since length = 20 cm, height = 10 cm, and base side = 10 cm the sides are: - 2 sides with dimensions Height x Length: $2 \times (10 \times 20) = 2 \times 200 = 400 \text{ cm}^2$ - 2 sides with dimensions Height x Base: $2 \times (10 \times 10) = 2 \times 100 = 200 \text{ cm}^2$ 4. Sum all areas: $$\text{Total Surface Area} = \text{base} + \text{top} + \text{sides} = 100 + 100 + 400 + 200 = 800 \text{ cm}^2$$ 5. However, the question states net area is 1600 cm^2. Usually, 'net' here refers to the unfolded cardboard sheet for the closed box, which may include all faces. Let's reconsider: The rectangular prism has 6 faces: 2 square bases and 4 rectangular lateral faces. - Each square base: $10 \times 10 = 100$ cm^2, so two bases total: $2 \times 100 = 200$ cm^2 - The 4 rectangular faces: - Two of size $10 \times 20$ each: $2 \times 200 = 400$ cm$^2$ - Two of size $10 \times 20$ each: $2 \times 200 = 400$ cm$^2$ Sum all the areas: $$200 + 400 + 400 = 1000 \text{ cm}^2$$ which is still not 1600. Could it be that Length and Base might have different interpretations? Assuming the base is indeed square with side 10 cm; height = 10 cm; length = 20 cm. Surface area of the rectangular prism: $$ 2(lb + bh + hl)$$ where $l=20$, $b=10$, $h=10$ Calculate each part: $$lb = 20 \times 10 = 200$$ $$bh = 10 \times 10 = 100$$ $$hl = 10 \times 20 = 200$$ Sum inside bracket: $$200 + 100 + 200 = 500$$ Multiply by 2: $$2 \times 500 = 1000 \text{ cm}^2$$ (total surface area) This conflicts with the required 1600. Possibly, 'net' refers to the entire cardboard sheet comprising multiple nets. Alternatively, perhaps the net means areas of all faces unfolded and additional parts (like flaps) totaling 1600 cm^2. Otherwise, if we calculate the net area of a box measuring 10 cm height, 10 cm base width, and 20 cm length, the total surface area is 1000 cm^2. 6. Conclusion: Based on standard formula, the rectangular cardboard sheet (net) area with given dimensions is $1000 \text{ cm}^2$, not 1600 cm^2. If the problem expects 1600, additional information or parts must be considered. Final calculated area of the net: $$\boxed{1000 \text{ cm}^2}$$