The formula for the surface area \( S \) of a right rectangular prism is given by:
\[ S = 2(lw + lh + wh) \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given:
- Length \( l = 4.5 , \text{cm} \)
- Width \( w = 3.5 , \text{cm} \)
- Height \( h = 2.5 , \text{cm} \)
Let's calculate each term:
- \( lw = 4.5 , \text{cm} \times 3.5 , \text{cm} = 15.75 , \text{cm}^2 \)
- \( lh = 4.5 , \text{cm} \times 2.5 , \text{cm} = 11.25 , \text{cm}^2 \)
- \( wh = 3.5 , \text{cm} \times 2.5 , \text{cm} = 8.75 , \text{cm}^2 \)
Now, add these areas together:
\[ lw + lh + wh = 15.75 , \text{cm}^2 + 11.25 , \text{cm}^2 + 8.75 , \text{cm}^2 = 35.75 , \text{cm}^2 \]
Finally, use the formula for surface area:
\[ S = 2 \times 35.75 , \text{cm}^2 = 71.5 , \text{cm}^2 \]
Thus, the surface area of the right rectangular prism is \( 71.5 , \text{cm}^2 \).