Question

What is the total surface area of a rectangular prism with sides 3 cm, 4 cm, and 5 cm?

Answer 1

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

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

where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.

Given the dimensions:
- Length (\( l \)) = 3 cm
- Width (\( w \)) = 4 cm
- Height (\( h \)) = 5 cm

Now, substitute the values into the formula:

1. Calculate the areas of each pair of faces:
- \( lw = 3 \times 4 = 12 \) cm²
- \( lh = 3 \times 5 = 15 \) cm²
- \( wh = 4 \times 5 = 20 \) cm²

2. Now sum these areas:
\[
lw + lh + wh = 12 + 15 + 20 = 47 \text{ cm}^2
\]

3. Now multiply by 2 to get the total surface area:
\[
\text{Surface Area} = 2 \times 47 = 94 \text{ cm}^2
\]

Thus, the total surface area of the rectangular prism is \(\boxed{94} \, \text{cm}^2\).