To find the surface area of a right rectangular prism, you can use the formula:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where \( l \), \( w \), and \( h \) represent the length, width, and height of the prism, respectively.
Since all edges of the prism measure 12.75 cm, we have:
- \( l = 12.75 , \text{cm} \)
- \( w = 12.75 , \text{cm} \)
- \( h = 12.75 , \text{cm} \)
Now we can substitute the values into the formula:
\[ \text{Surface Area} = 2(12.75 \cdot 12.75 + 12.75 \cdot 12.75 + 12.75 \cdot 12.75) \]
Calculating each term inside the parentheses:
\[ 12.75 \cdot 12.75 = 162.5625 \]
So we have:
\[ \text{Surface Area} = 2(162.5625 + 162.5625 + 162.5625) \] \[ \text{Surface Area} = 2(3 \times 162.5625) \] \[ \text{Surface Area} = 2(487.6875) \] \[ \text{Surface Area} = 975.375 , \text{cm}^2 \]
Therefore, the surface area of the right rectangular prism is \( 975.375 , \text{cm}^2 \).