Question

What is the surface area of the rectangular prism?

How to solve for surface area

Answer 1

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

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

where:
- \( l \) = length of the prism
- \( w \) = width of the prism
- \( h \) = height of the prism

### Steps to Solve for Surface Area:
1. **Identify the dimensions** of the rectangular prism: length (\(l\)), width (\(w\)), and height (\(h\)).
2. **Calculate the area of each pair of opposite faces**:
- \( lw \): the area of the bottom and top faces.
- \( lh \): the area of the front and back faces.
- \( wh \): the area of the left and right faces.
3. **Sum these areas**: Add the areas calculated from step 2 together.
4. **Multiply by 2**: Since the prism has two of each face, you multiply the sum by 2 to get the total surface area.

### Example:
Suppose the dimensions of a rectangular prism are \( l = 5 \) units, \( w = 3 \) units, and \( h = 4 \) units.

1. Calculate the areas:
- \( lw = 5 \times 3 = 15 \) square units
- \( lh = 5 \times 4 = 20 \) square units
- \( wh = 3 \times 4 = 12 \) square units

2. Sum the areas:
\[
lw + lh + wh = 15 + 20 + 12 = 47 \quad \text{square units}
\]

3. Multiply by 2 to find the surface area:
\[
\text{Surface Area} = 2 \times 47 = 94 \quad \text{square units}
\]

So, the surface area of the rectangular prism is \( 94 \) square units.