To find the total surface area of a rectangular box (or 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 box.
In this case:
- Length (\( l \)) = 3 feet
- Width (\( w \)) = 2 feet
- Height (\( h \)) = 4 feet
Now, plug these values into the formula:
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Calculate \( lw \): \[ lw = 3 \times 2 = 6 \text{ square feet} \]
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Calculate \( lh \): \[ lh = 3 \times 4 = 12 \text{ square feet} \]
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Calculate \( wh \): \[ wh = 2 \times 4 = 8 \text{ square feet} \]
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Now sum these areas: \[ lw + lh + wh = 6 + 12 + 8 = 26 \text{ square feet} \]
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Finally, multiply by 2 to find the total surface area: \[ \text{Surface Area} = 2 \times 26 = 52 \text{ square feet} \]
Therefore, the total surface area of the box is 52 square feet.