Question

Use the formula to determine the surface area of a right rectangular prism where each edge length measures 12.75 cm.(1 point)
Responses

975.38 cm2
975.38

cm
2
975.38 cm squared

76.5 cm2
76.5

cm
2
76.5 cm squared

5,852.25 cm2
5
,
852.25

cm
2
5,852.25 cm squared

459 cm2

Answer 1

To find the surface area of a right rectangular prism, we 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. In this case, since all edge lengths are equal, we can denote each edge length as \(s = 12.75 \, \text{cm}\).

Thus, we can redefine the surface area formula for a cube (which is a special type of rectangular prism) as:

\[
\text{Surface Area} = 6s^2
\]

Now substituting \(s = 12.75 \, \text{cm}\):

\[
\text{Surface Area} = 6(12.75)^2
\]
\[
= 6(162.5625)
\]
\[
= 975.375 \, \text{cm}^2
\]

Rounding to two decimal places, the surface area is:

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

Therefore, the correct response from your options is:

**975.38 cm²**