To find the surface area of a right rectangular prism, we use the formula:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
Given:
- Length \( l = 4.5 , \text{cm} \)
- Width \( w = 3.5 , \text{cm} \)
- Height \( h = 2.5 , \text{cm} \)
Now we can calculate each of the components:
- \( lw = 4.5 \times 3.5 = 15.75 , \text{cm}^2 \)
- \( lh = 4.5 \times 2.5 = 11.25 , \text{cm}^2 \)
- \( wh = 3.5 \times 2.5 = 8.75 , \text{cm}^2 \)
Adding these up:
\[ lw + lh + wh = 15.75 + 11.25 + 8.75 = 35.75 , \text{cm}^2 \]
Now, multiply by 2 to find the total surface area:
\[ \text{Surface Area} = 2 \times 35.75 = 71.5 , \text{cm}^2 \]
Therefore, the surface area of the rectangular prism is 71.5 cm².