Kaylee found the surface area, in square inches, of a rectangular prism by using this formula:
[tex]\[
2(5 \times 3) + 2(5 \times 8) + 2(3 \times 8)
\][/tex]

What is the surface area of the prism, in square inches?

A. 85
B. 40
C. 158
D. 238



Answer :

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]