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 prism.
First, we need to identify the dimensions:
- Length ([tex]\( l \)[/tex]) = 5 inches
- Width ([tex]\( w \)[/tex]) = 3 inches
- Height ([tex]\( h \)[/tex]) = 8 inches
Now, substitute these dimensions into the formula and calculate each term separately.
1. Calculate [tex]\( lw \)[/tex]:
[tex]\[
lw = 5 \times 3 = 15
\][/tex]
2. Calculate [tex]\( lh \)[/tex]:
[tex]\[
lh = 5 \times 8 = 40
\][/tex]
3. Calculate [tex]\( wh \)[/tex]:
[tex]\[
wh = 3 \times 8 = 24
\][/tex]
Add these products together:
[tex]\[
lw + lh + wh = 15 + 40 + 24 = 79
\][/tex]
Now multiply by 2 (since the formula is [tex]\( 2(lw + lh + wh) \)[/tex]):
[tex]\[
2 \times 79 = 158
\][/tex]
So, the surface area of the prism is:
[tex]\[ 158 \text{ square inches} \][/tex]
Therefore, the correct answer is:
[tex]\[ 158 \][/tex]
