To find the surface area of a rectangular box (or a rectangular prism), we 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:
- \( l = 12.5 \) inches,
- \( w = 3.0 \) inches,
- \( h = 9.5 \) inches.
Now we can calculate the surface area step by step.
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Calculate each term:
- \( lw = 12.5 \times 3.0 = 37.5 \) square inches
- \( lh = 12.5 \times 9.5 = 118.75 \) square inches
- \( wh = 3.0 \times 9.5 = 28.5 \) square inches
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Sum those areas: \[ lw + lh + wh = 37.5 + 118.75 + 28.5 = 184.75 \text{ square inches} \]
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Finally, multiply by 2: \[ \text{Surface Area} = 2 \times 184.75 = 369.5 \text{ square inches} \]
The surface area of the box is 369.5 square inches.