To find the surface area of a rectangular prism, we can use the formula:
[tex]\[ \text{Surface Area} = 2lw + 2lh + 2wh \][/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.
Given the dimensions provided:
- Length ([tex]\( l \)[/tex]) = 5 inches
- Width ([tex]\( w \)[/tex]) = 3 inches
- Height ([tex]\( h \)[/tex]) = 8 inches
Substitute these values into the formula:
1. Calculate [tex]\( 2lw \)[/tex]:
[tex]\[ 2(lw) = 2(5 \times 3) = 2 \times 15 = 30 \][/tex]
2. Calculate [tex]\( 2lh \)[/tex]:
[tex]\[ 2(lh) = 2(5 \times 8) = 2 \times 40 = 80 \][/tex]
3. Calculate [tex]\( 2wh \)[/tex]:
[tex]\[ 2(wh) = 2(3 \times 8) = 2 \times 24 = 48 \][/tex]
Now, add these three results together to find the total surface area:
[tex]\[ 30 + 80 + 48 = 158 \][/tex]
Therefore, the surface area of the rectangular prism is:
[tex]\[ \boxed{158} \][/tex] square inches.
