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 \(h\) are the lengths of the edges of the prism.
Given that all edges of the prism measure 12.75 cm, we have:
\(l = 12.75 , \text{cm}\),
\(w = 12.75 , \text{cm}\),
\(h = 12.75 , \text{cm}\).
Plugging in the values:
\[ \text{Surface Area} = 2(12.75 \times 12.75 + 12.75 \times 12.75 + 12.75 \times 12.75) \]
Calculating \(12.75 \times 12.75\):
\[ 12.75 \times 12.75 = 162.5625 \]
Now, substituting back into the surface area formula:
\[ \text{Surface Area} = 2(162.5625 + 162.5625 + 162.5625) = 2(487.6875) \]
Then, calculate:
\[ \text{Surface Area} = 975.375 , \text{cm}^2 \]
Rounding this to two decimal places gives:
\[ \text{Surface Area} \approx 975.38 , \text{cm}^2 \]
Thus, the answer is 975.38 cm².