Question

Use the formula to determine the surface area of a right rectangular prism where each edge length
measures 12.75 cm.(1 point)
459 cm2 459 cm2
5, 852.25 cm2 5, 852.25 cm2
975.38 cm2 975.38 cm2
76.5 cm2

Answer 1

To calculate the surface area of a right rectangular prism (also known as a rectangular cuboid), we use the formula:

\[
\text{Surface Area} = 2(lw + lh + wh)
\]

where:
- \( l \) is the length
- \( w \) is the width
- \( h \) is the height

In this case, since all edge lengths of the prism are equal and measure 12.75 cm (making it a cube), we can simplify the formula as follows:

Let \( l = w = h = 12.75 \, \text{cm} \).

The surface area calculation will be:

\[
\text{Surface Area} = 2(12.75 \times 12.75 + 12.75 \times 12.75 + 12.75 \times 12.75)
\]
\[
= 2(3 \times (12.75 \times 12.75))
\]
\[
= 2(3 \times 162.5625)
\]
\[
= 2(487.6875)
\]
\[
= 975.375 \, \text{cm}^2
\]

Rounding it to two decimal places gives us:

\[
\text{Surface Area} \approx 975.38 \, \text{cm}^2
\]

Therefore, the correct answer is **975.38 cm²**.