Question

6 what is the surface area of a rectangular prism whose length = 4 inches, width = 6 inches, and height = 4 inches?
144 inches squared
40 inches squared
96 inches squared
128 inches squared
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Explanation:

Step1: Recall the formula for the surface area of a rectangular prism.

The formula for the surface area \( SA \) of a rectangular prism is \( SA = 2(lw + lh + wh) \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height.

Step2: Substitute the given values into the formula.

Given \( l = 4 \) inches, \( w = 6 \) inches, and \( h = 4 \) inches.
First, calculate \( lw \), \( lh \), and \( wh \):

• \( lw = 4 \times 6 = 24 \)
• \( lh = 4 \times 4 = 16 \)
• \( wh = 6 \times 4 = 24 \)

Then, substitute these into the formula:
\( SA = 2(24 + 16 + 24) \)

Step3: Simplify the expression inside the parentheses.

\( 24 + 16 + 24 = 64 \)

Step4: Multiply by 2.

\( SA = 2 \times 64 = 128 \)

Answer:

128 inches squared