To find the total surface area of a rectangular prism, you can use the formula:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where \( l \), \( w \), and \( h \) are the lengths of the sides of the prism.
Given the sides of the rectangular prism:
- \( l = 5 \) cm
- \( w = 4 \) cm
- \( h = 2 \) cm
Now, we can calculate the surface area step by step.
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Calculate the area of each pair of sides:
- \( lw = 5 \times 4 = 20 \) cm²
- \( lh = 5 \times 2 = 10 \) cm²
- \( wh = 4 \times 2 = 8 \) cm²
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Sum these areas: \[ lw + lh + wh = 20 + 10 + 8 = 38 , \text{cm}^2 \]
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Now, multiply by 2 to get the total surface area: \[ \text{Surface Area} = 2 \times 38 = 76 , \text{cm}^2 \]
Thus, the total surface area of the rectangular prism is \( \boxed{76} \) cm².