Answered

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
B. 238
C. 40
D. 85



Answer :

GinnyAnswer
To find the surface area of a rectangular prism, we use the formula:

[tex]\[ 2 \cdot ( \text{length} \cdot \text{width} ) + 2 \cdot ( \text{length} \cdot \text{height} ) + 2 \cdot ( \text{width} \cdot \text{height} ) \][/tex]

Given dimensions:
- Length ([tex]\( l \)[/tex]) = 5 inches
- Width ([tex]\( w \)[/tex]) = 3 inches
- Height ([tex]\( h \)[/tex]) = 8 inches

Let's break down the calculation step-by-step:

1. Calculate the area of the pairs of rectangular sides:

[tex]\[ \text{First pair of opposite sides: } 2 \cdot ( l \cdot w ) \][/tex]
[tex]\[ 2 \cdot ( 5 \cdot 3 ) = 2 \cdot 15 = 30 \text{ square inches} \][/tex]

[tex]\[ \text{Second pair of opposite sides: } 2 \cdot ( l \cdot h ) \][/tex]
[tex]\[ 2 \cdot ( 5 \cdot 8 ) = 2 \cdot 40 = 80 \text{ square inches} \][/tex]

[tex]\[ \text{Third pair of opposite sides: } 2 \cdot ( w \cdot h ) \][/tex]
[tex]\[ 2 \cdot ( 3 \cdot 8 ) = 2 \cdot 24 = 48 \text{ square inches} \][/tex]

2. Add the areas of all three pairs of opposite sides together:

[tex]\[ \text{Total Surface Area} = 30 \text{ square inches} + 80 \text{ square inches} + 48 \text{ square inches} \][/tex]
[tex]\[ \text{Total Surface Area} = 158 \text{ square inches} \][/tex]

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

Looking at the multiple-choice options, the correct answer is:

[tex]\[ \text{158} \][/tex]

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