Subjects geometry

Surface Area 410F7E

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1. **State the problem:** Calculate the surface area of a rectangular prism with dimensions 4 cm (height), 3 cm (width), and 50 mm (length). 2. **Convert all dimensions to the same unit:** Since 50 mm = 5 cm, the dimensions are 4 cm, 3 cm, and 5 cm. 3. **Recall the surface area formula for a rectangular prism:** $$SA = 2(lw + lh + wh)$$ where $l$, $w$, and $h$ are the length, width, and height respectively. 4. **Substitute the values:** $$SA = 2(5 \times 3 + 5 \times 4 + 3 \times 4)$$ 5. **Calculate each product:** $$5 \times 3 = 15$$ $$5 \times 4 = 20$$ $$3 \times 4 = 12$$ 6. **Sum the products:** $$15 + 20 + 12 = 47$$ 7. **Multiply by 2:** $$SA = 2 \times 47 = 94$$ 8. **Final answer:** $$SA = 94\text{ cm}^2$$ The surface area of the rectangular prism is 94 cm².