To find the surface area of a rectangular prism, we use the formula:
[tex]\[ \text{Surface Area} = 2(lw + lh + wh) \][/tex]
where [tex]\( l \)[/tex] is the length, [tex]\( w \)[/tex] is the width, and [tex]\( h \)[/tex] is the height of the rectangular prism. In this case, the gift dimensions are:
- Length ([tex]\( l \)[/tex]) = 8 inches
- Width ([tex]\( w \)[/tex]) = 6 inches
- Height ([tex]\( h \)[/tex]) = 10 inches
Substituting these values into the formula, we get:
[tex]\[ \text{Surface Area} = 2(8 \cdot 6 + 8 \cdot 10 + 6 \cdot 10) \][/tex]
First, we calculate the three areas:
[tex]\[ 8 \cdot 6 = 48 \][/tex]
[tex]\[ 8 \cdot 10 = 80 \][/tex]
[tex]\[ 6 \cdot 10 = 60 \][/tex]
Next, we add these areas together:
[tex]\[ 48 + 80 + 60 = 188 \][/tex]
Then, we multiply this sum by 2:
[tex]\[ 2 \cdot 188 = 376 \][/tex]
Therefore, the surface area that Casey needs to wrap is:
[tex]\[ 376 \, \text{in.}^2 \][/tex]
Among the given options, the correct one is:
[tex]\[ 376 \, \text{in.}^2 \][/tex]
