The formula for the surface area \( SA \) of a right rectangular prism is given by:
\[ SA = 2(lw + lh + wh) \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Given the dimensions:
- Length \( l = 4.5 \) cm,
- Width \( w = 3.5 \) cm,
- Height \( h = 2.5 \) cm.
Let's plug the values into the formula:
-
Calculate \( lw \): \[ lw = 4.5 \times 3.5 = 15.75 , \text{cm}^2 \]
-
Calculate \( lh \): \[ lh = 4.5 \times 2.5 = 11.25 , \text{cm}^2 \]
-
Calculate \( wh \): \[ wh = 3.5 \times 2.5 = 8.75 , \text{cm}^2 \]
Now, add these areas together: \[ lw + lh + wh = 15.75 + 11.25 + 8.75 = 35.75 , \text{cm}^2 \]
Finally, multiply by 2 to find the surface area: \[ SA = 2 \times 35.75 = 71.5 , \text{cm}^2 \]
So, the surface area of the right rectangular prism is \( \boxed{71.5 , \text{cm}^2} \).