The surface area \( A \) of a right rectangular prism can be calculated using the formula:
\[ A = 2(lw + lh + wh) \]
where \( l \), \( w \), and \( h \) are the lengths of the edges of the prism.
In this case, each edge length measures 12.75 cm, so:
- \( l = 12.75 \) cm
- \( w = 12.75 \) cm
- \( h = 12.75 \) cm
Now plug these values into the formula:
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Calculate \( lw \), \( lh \), and \( wh \): \[ lw = 12.75 \times 12.75 = 162.5625 , \text{cm}^2 \] \[ lh = 12.75 \times 12.75 = 162.5625 , \text{cm}^2 \] \[ wh = 12.75 \times 12.75 = 162.5625 , \text{cm}^2 \]
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Now add these values together: \[ lw + lh + wh = 162.5625 + 162.5625 + 162.5625 = 487.6875 , \text{cm}^2 \]
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Finally, substitute this sum back into the surface area formula: \[ A = 2 \times 487.6875 = 975.375 , \text{cm}^2 \]
Rounding to two decimal places, the surface area is:
\[ A \approx 975.38 , \text{cm}^2 \]
Therefore, the correct response is 975.38 cm².