To find out how much wrapping paper Jerry needs to wrap the present, we need to calculate the surface area of the box. The formula for the surface area \( SA \) of a rectangular box (or rectangular prism) is given by:
\[ SA = 2lw + 2lh + 2wh \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given:
- \( l = 17 \) cm,
- \( w = 10 \) cm,
- \( h = 4 \) cm.
Now we can plug these values into the surface area formula:
\[ SA = 2(17 \text{ cm} \times 10 \text{ cm}) + 2(17 \text{ cm} \times 4 \text{ cm}) + 2(10 \text{ cm} \times 4 \text{ cm}) \]
Calculating each term:
- \( 2(17 \times 10) = 2(170) = 340 \text{ cm}^2 \)
- \( 2(17 \times 4) = 2(68) = 136 \text{ cm}^2 \)
- \( 2(10 \times 4) = 2(40) = 80 \text{ cm}^2 \)
Now sum these areas:
\[ SA = 340 + 136 + 80 = 556 \text{ cm}^2 \]
Therefore, Jerry needs 556 cm² of wrapping paper to wrap the present.