To find the amount of wrapping paper needed to wrap the present, we need to calculate the surface area of the box. The box measures 10 cm wide, 4 cm high, and 17 cm long.
The formula for the surface area \( A \) of a rectangular box is:
\[ A = 2(lw + lh + wh) \]
where:
- \( l \) is the length,
- \( w \) is the width, and
- \( h \) is the height.
Substituting the values:
- \( l = 17 \) cm
- \( w = 10 \) cm
- \( h = 4 \) cm
Now, let's calculate each term:
- \( lw = 17 \times 10 = 170 \) cm²
- \( lh = 17 \times 4 = 68 \) cm²
- \( wh = 10 \times 4 = 40 \) cm²
Now, add these products together:
\[ lw + lh + wh = 170 + 68 + 40 = 278 \text{ cm}^2 \]
Now, multiply this sum by 2 to find the total surface area:
\[ A = 2 \times 278 = 556 \text{ cm}^2 \]
Therefore, Jerry needs 556 cm² of wrapping paper to wrap the present.