Subjects geometry

Surface Area Prisms A9C7D3

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1. The problem is to verify the surface area calculations of three rectangular prisms. 2. The formula for the surface area $SA$ of a rectangular prism with length $l$, width $w$, and height $h$ is: $$SA = 2(lw + lh + wh)$$ 3. For the first prism (cube-like) with edges 4 cm: $$SA = 2(4\times4 + 4\times4 + 4\times4) = 2(16 + 16 + 16) = 2(48) = 96\text{ cm}^2$$ 4. For the second prism with dimensions 6 m, 8 m, and 3 m: $$SA = 2(8\times6 + 3\times6 + 8\times3) = 2(48 + 18 + 24) = 2(90) = 180\text{ m}^2$$ 5. For the third prism with base edges 5 cm and 5 cm and height 11 cm: $$SA = 2(5\times5 + 5\times11 + 5\times11) = 2(25 + 55 + 55) = 2(135) = 270\text{ cm}^2$$ 6. All surface area calculations are correct as given. Final answer: The surface areas 96 cm², 180 m², and 270 cm² are correct for the given prisms.