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.
-
Calculate \( 2lw \): \[ 2lw = 2 \cdot 9 \cdot 3 = 54 \text{ in}^2 \]
-
Calculate \( 2lh \): \[ 2lh = 2 \cdot 9 \cdot 5 = 90 \text{ in}^2 \]
-
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
\[ \boxed{174} \text{ in}^2 \]