Question

A rectangular prism has a length of 7 cm, a width of 3 cm, and a height of 2 cm. What is its total surface area?

Answer 1

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

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

Where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.

Given:
- Length (\( l \)) = 7 cm
- Width (\( w \)) = 3 cm
- Height (\( h \)) = 2 cm

Now, let's calculate each area:

1. Calculate \( lw \):
\[
lw = 7 \, \text{cm} \times 3 \, \text{cm} = 21 \, \text{cm}^2
\]

2. Calculate \( lh \):
\[
lh = 7 \, \text{cm} \times 2 \, \text{cm} = 14 \, \text{cm}^2
\]

3. Calculate \( wh \):
\[
wh = 3 \, \text{cm} \times 2 \, \text{cm} = 6 \, \text{cm}^2
\]

Now, substitute these values into the surface area formula:

\[
\text{Surface Area} = 2(21 \, \text{cm}^2 + 14 \, \text{cm}^2 + 6 \, \text{cm}^2)
\]

Calculating the sum inside the parentheses:

\[
21 \, \text{cm}^2 + 14 \, \text{cm}^2 + 6 \, \text{cm}^2 = 41 \, \text{cm}^2
\]

Now, multiply by 2:

\[
\text{Surface Area} = 2 \times 41 \, \text{cm}^2 = 82 \, \text{cm}^2
\]

Thus, the total surface area of the rectangular prism is:

\[
\boxed{82 \, \text{cm}^2}
\]