To determine how much wrapping paper Anton will need, we need to calculate the surface area (SA) of the box using the formula given:
\[ SA = 2(lw + lh + wh) \]
where:
- \( l = 17 , \text{cm} \) (length)
- \( w = 10 , \text{cm} \) (width)
- \( h = 4 , \text{cm} \) (height)
Now, let's calculate each term inside the parentheses:
- \( lw = 17 \times 10 = 170 , \text{cm}^2 \)
- \( lh = 17 \times 4 = 68 , \text{cm}^2 \)
- \( wh = 10 \times 4 = 40 , \text{cm}^2 \)
Now, we can add these values together:
\[ lw + lh + wh = 170 + 68 + 40 = 278 , \text{cm}^2 \]
Next, we apply this to the formula for surface area:
\[ SA = 2 \times 278 = 556 , \text{cm}^2 \]
Thus, Anton will need 556 cm² of wrapping paper to wrap the present.