Question

surface area of right rectangular prism with each edge length of 12.75

Answer 1

To find the surface area of a right rectangular prism (also known as a rectangular box), 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.

In this case, if each edge length is 12.75, then:

- \( l = 12.75 \)
- \( w = 12.75 \)
- \( h = 12.75 \)

Now plug the values into the formula:

\[
\text{Surface Area} = 2(12.75 \times 12.75 + 12.75 \times 12.75 + 12.75 \times 12.75)
\]

This simplifies to:

\[
\text{Surface Area} = 2(3 \times 12.75^2)
\]

Now calculate \( 12.75^2 \):

\[
12.75^2 = 162.5625
\]

Then substitute this back into the equation:

\[
\text{Surface Area} = 2(3 \times 162.5625)
\]

Calculate \( 3 \times 162.5625 \):

\[
3 \times 162.5625 = 487.6875
\]

Now, multiply by 2:

\[
\text{Surface Area} = 2 \times 487.6875 = 975.375
\]

So, the surface area of the right rectangular prism is:

\[
\boxed{975.375} \text{ square units}
\]