A rectangular prism is 2 meters long, 3 meters wide, and 3.3 meters high. What is the surface area of the rectangular prism?

1. Break Down the Problem

To find the surface area of the rectangular prism, we need to use the formula for the surface area $S$ of a rectangular prism: $S = 2(lw + lh + wh)$ where:

• $l$ is the length,
• $w$ is the width,
• $h$ is the height.

2. Relevant Concepts

Given:

• Length $l = 2$ meters,
• Width $w = 3$ meters,
• Height $h = 3.3$ meters.

3. Analysis and Detail

Substituting the values into the surface area formula: $S = 2(lw + lh + wh)$ Calculating each component:

1. Calculate $lw$: $lw = 2 \times 3 = 6 \, \text{m}^2$

2. Calculate $lh$: $lh = 2 \times 3.3 = 6.6 \, \text{m}^2$

3. Calculate $wh$: $wh = 3 \times 3.3 = 9.9 \, \text{m}^2$

Adding these areas together: $lw + lh + wh = 6 + 6.6 + 9.9 = 22.5 \, \text{m}^2$

Now, calculating the total surface area $S$: $S = 2 \times 22.5 = 45 \, \text{m}^2$

4. Verify and Summarize

We have calculated all components correctly. The individual area calculations:

• $lw = 6 \, \text{m}^2$
• $lh = 6.6 \, \text{m}^2$
• $wh = 9.9 \, \text{m}^2$

Add up to $22.5 \, \text{m}^2$, multiplied by 2 gives the surface area $S$.

Final Answer

The surface area of the rectangular prism is $45 \, \text{m}^2$.