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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. 158

Sagot :

GinnyAnsweridn
Sure! Let's break down the calculation of the surface area of a rectangular prism using the given formula:

The formula for the surface area of a rectangular prism is:
[tex]\[ 2(lw) + 2(lh) + 2(wh) \][/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.

Here are the given dimensions of the rectangular prism:
- Length ([tex]\( l \)[/tex]) = 5 inches
- Width ([tex]\( w \)[/tex]) = 3 inches
- Height ([tex]\( h \)[/tex]) = 8 inches

Now let's break down each term in the formula:
1. First, we calculate [tex]\( lw \)[/tex]:
[tex]\[ lw = 5 \times 3 = 15 \][/tex]
Then we multiply by 2:
[tex]\[ 2(lw) = 2 \times 15 = 30 \][/tex]

2. Next, we calculate [tex]\( lh \)[/tex]:
[tex]\[ lh = 5 \times 8 = 40 \][/tex]
Then we multiply by 2:
[tex]\[ 2(lh) = 2 \times 40 = 80 \][/tex]

3. Finally, we calculate [tex]\( wh \)[/tex]:
[tex]\[ wh = 3 \times 8 = 24 \][/tex]
Then we multiply by 2:
[tex]\[ 2(wh) = 2 \times 24 = 48 \][/tex]

Now, we sum all these terms together to find the total surface area:
[tex]\[ 30 + 80 + 48 = 158 \][/tex]

Thus, the surface area of the prism is [tex]\( 158 \)[/tex] square inches.
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