The figure is the net for a rectangular prism.

What is the surface area of the rectangular prism represented by the net?



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in²

An unfolded rectangular prism with a length of nine inches labeling the top and bottom, a width of three inches labeling the sides and arrows pointing to the other sides for the height measuring five inches.

1 answer

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

\[ \text{Surface Area} = 2lw + 2lh + 2wh \]

where:

  • \( l \) is the length,
  • \( w \) is the width,
  • \( h \) is the height.

From the information given:

  • Length (\( l \)) = 9 inches
  • Width (\( w \)) = 3 inches
  • Height (\( h \)) = 5 inches

Let's calculate each term step by step.

  1. Calculate \( 2lw \): \[ 2lw = 2 \cdot 9 \cdot 3 = 54 \text{ in}^2 \]

  2. Calculate \( 2lh \): \[ 2lh = 2 \cdot 9 \cdot 5 = 90 \text{ in}^2 \]

  3. Calculate \( 2wh \): \[ 2wh = 2 \cdot 3 \cdot 5 = 30 \text{ in}^2 \]

Now, sum these areas to find the total surface area:

\[ \text{Surface Area} = 2lw + 2lh + 2wh = 54 + 90 + 30 = 174 \text{ in}^2 \]

Thus, the surface area of the rectangular prism is

\[ \boxed{174} \text{ in}^2 \]