To calculate the surface area of the rectangular prism (the box Jerry is using to wrap the present), we can use the formula for the surface area of a rectangular prism:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given the dimensions:
- Length (\( l \)) = 17 cm
- Width (\( w \)) = 10 cm
- Height (\( h \)) = 4 cm
Now we can substitute these values into the formula:
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Calculate \( lw \): \[ lw = 17 , \text{cm} \times 10 , \text{cm} = 170 , \text{cm}^2 \]
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Calculate \( lh \): \[ lh = 17 , \text{cm} \times 4 , \text{cm} = 68 , \text{cm}^2 \]
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Calculate \( wh \): \[ wh = 10 , \text{cm} \times 4 , \text{cm} = 40 , \text{cm}^2 \]
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Now add these areas: \[ lw + lh + wh = 170 , \text{cm}^2 + 68 , \text{cm}^2 + 40 , \text{cm}^2 = 278 , \text{cm}^2 \]
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Finally, calculate the total surface area: \[ \text{Surface Area} = 2 \times 278 , \text{cm}^2 = 556 , \text{cm}^2 \]
Therefore, the amount of wrapping paper Jerry will need to wrap the present is:
\[ \text{Surface Area} = 556 , \text{cm}^2 \]