To determine how much wrapping paper Jenny will need to wrap the box, we need to calculate the surface area of the box. The box is a rectangular prism, and its surface area \( S \) can be calculated using the formula:
\[ S = 2lw + 2lh + 2wh \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the box.
Given the dimensions of the box:
- Length \( l = 17 \) cm
- Width \( w = 10 \) cm
- Height \( h = 4 \) cm
Substituting these values into the surface area formula:
\[ S = 2(17 \times 10) + 2(17 \times 4) + 2(10 \times 4) \]
Calculating each term step by step:
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Calculate \( 17 \times 10 \): \[ 17 \times 10 = 170 \]
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Calculate \( 17 \times 4 \): \[ 17 \times 4 = 68 \]
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Calculate \( 10 \times 4 \): \[ 10 \times 4 = 40 \]
Now substituting these values back into the surface area formula:
\[ S = 2(170) + 2(68) + 2(40) \]
Calculating each part:
- \( 2 \times 170 = 340 \)
- \( 2 \times 68 = 136 \)
- \( 2 \times 40 = 80 \)
Now, adding these values together:
\[ S = 340 + 136 + 80 \]
Calculating the total:
\[ S = 556 \]
Thus, the total surface area of the box is \( 556 \) cm².
Therefore, Jenny will need 556 cm² of wrapping paper to wrap the present.