To find the surface area \( S \) of a right rectangular prism, you can use the formula:
\[ S = 2(lw + lh + wh) \]
where \( l \), \( w \), and \( h \) are the lengths of the edges of the prism.
In this case, all edge lengths are the same, given as:
- Length \( l = 12.75 , cm \)
- Width \( w = 12.75 , cm \)
- Height \( h = 12.75 , cm \)
Now, we substitute the values into the formula:
\[ S = 2(lw + lh + wh) = 2(12.75 \cdot 12.75 + 12.75 \cdot 12.75 + 12.75 \cdot 12.75) \]
First, calculate \( lw \), \( lh \), and \( wh \):
\[ lw = 12.75 \cdot 12.75 = 162.5625 \] \[ lh = 12.75 \cdot 12.75 = 162.5625 \] \[ wh = 12.75 \cdot 12.75 = 162.5625 \]
Now, sum those products:
\[ lw + lh + wh = 162.5625 + 162.5625 + 162.5625 = 487.6875 \]
Now, we calculate the total surface area:
\[ S = 2(487.6875) = 975.375 , cm^2 \]
Rounding to two decimal places gives us:
\[ S \approx 975.38 , cm^2 \]
Thus, the correct response for the surface area is \( 975.38 , cm^2 \).