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,
- \( h \) is the height.
Given the dimensions:
- \( h = 2 \) cm,
- \( w = 4 \) cm,
- \( l = 5 \) cm.
Now, let's calculate it step by step:
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Calculate \( lw \): \[ lw = 5 \times 4 = 20 \]
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Calculate \( lh \): \[ lh = 5 \times 2 = 10 \]
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Calculate \( wh \): \[ wh = 4 \times 2 = 8 \]
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Now sum these values: \[ lw + lh + wh = 20 + 10 + 8 = 38 \]
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Finally, plug it into the surface area formula: \[ \text{Surface Area} = 2 \times 38 = 76 , \text{cm}^2 \]
Thus, the total surface area of the rectangular prism is \( 76 , \text{cm}^2 \).