To determine how much wrapping paper Liliana will need to wrap the present, we need to calculate the surface area of the box. The surface area \( A \) of a rectangular box can be calculated using the formula:
\[ A = 2lw + 2lh + 2wh \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given:
- Length \( l = 10 \) in,
- Width \( w = 3 \) in,
- Height \( h = 4 \) in.
Now we can plug in the values:
-
Calculate the area of the two length-width (lw) faces: \[ 2lw = 2 \times 10 \times 3 = 60 \text{ in}^2 \]
-
Calculate the area of the two length-height (lh) faces: \[ 2lh = 2 \times 10 \times 4 = 80 \text{ in}^2 \]
-
Calculate the area of the two width-height (wh) faces: \[ 2wh = 2 \times 3 \times 4 = 24 \text{ in}^2 \]
Now, add these areas together to get the total surface area:
\[ A = 60 + 80 + 24 = 164 \text{ in}^2 \]
Therefore, Liliana will need 164 in² of wrapping paper to wrap the present.
The correct answer is 164 in².