To find the total surface area of a rectangular prism, you can use the formula:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.
Given the dimensions:
- Length (\( l \)) = 3 cm
- Width (\( w \)) = 4 cm
- Height (\( h \)) = 5 cm
Now, substitute the values into the formula:
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Calculate the areas of each pair of faces:
- \( lw = 3 \times 4 = 12 \) cm²
- \( lh = 3 \times 5 = 15 \) cm²
- \( wh = 4 \times 5 = 20 \) cm²
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Now sum these areas: \[ lw + lh + wh = 12 + 15 + 20 = 47 \text{ cm}^2 \]
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Now multiply by 2 to get the total surface area: \[ \text{Surface Area} = 2 \times 47 = 94 \text{ cm}^2 \]
Thus, the total surface area of the rectangular prism is \(\boxed{94} , \text{cm}^2\).