Question

a rectangular prism has measurements of the basis 8 mm the height is 15 mm and the width is 15 mm. What is the surface area?

Answer 1

To find the surface area of a rectangular prism, you can use the formula:

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

where:
- \( l \) = length (or base),
- \( w \) = width, and
- \( h \) = height.

In your case, the dimensions are:
- Length (\( l \)) = 8 mm,
- Width (\( w \)) = 15 mm,
- Height (\( h \)) = 15 mm.

Now plug these values into the formula:

1. Calculate \( lw \):
\[
lw = 8 \, \text{mm} \times 15 \, \text{mm} = 120 \, \text{mm}^2
\]

2. Calculate \( lh \):
\[
lh = 8 \, \text{mm} \times 15 \, \text{mm} = 120 \, \text{mm}^2
\]

3. Calculate \( wh \):
\[
wh = 15 \, \text{mm} \times 15 \, \text{mm} = 225 \, \text{mm}^2
\]

Now, put all this into the surface area formula:

\[
\text{Surface Area} = 2(120 \, \text{mm}^2 + 120 \, \text{mm}^2 + 225 \, \text{mm}^2)
\]

Calculate the sum inside the parentheses:

\[
120 + 120 + 225 = 465 \, \text{mm}^2
\]

Now multiply by 2:

\[
\text{Surface Area} = 2 \times 465 \, \text{mm}^2 = 930 \, \text{mm}^2
\]

Thus, the surface area of the rectangular prism is **930 mm²**.