Subjects geometry

Surface Area Rectangular Prism 4C3128

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1. **State the problem:** We need to find the total surface area of the given figure, which appears to be a rectangular prism with dimensions 42 cm, 35 cm, and 9 cm. 2. **Formula for surface area of a rectangular prism:** $$\text{Surface Area} = 2(lw + lh + wh)$$ where $l$, $w$, and $h$ are the length, width, and height of the prism. 3. **Identify dimensions:** - Length $l = 42$ cm - Width $w = 35$ cm - Height $h = 9$ cm 4. **Calculate each product:** $$lw = 42 \times 35 = 1470$$ $$lh = 42 \times 9 = 378$$ $$wh = 35 \times 9 = 315$$ 5. **Sum the products:** $$1470 + 378 + 315 = 2163$$ 6. **Calculate total surface area:** $$\text{Surface Area} = 2 \times 2163 = 4326$$ 7. **Final answer:** The total surface area of the figure is $4326$ square centimeters.