The figure is the net for a rectangular prism.

Question

What is the surface area of the rectangular prism represented by the net?



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in²

An unfolded rectangular prism with a length of nine inches labeling the top and bottom, a width of three inches labeling the sides and arrows pointing to the other sides for the height measuring five inches.

Answer 1

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

$$\text{Surface Area}=2lw+2lh+2wh$$

where:

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

From the information given:

• Length ($l$) = 9 inches
• Width ($w$) = 3 inches
• Height ($h$) = 5 inches

Let's calculate each term step by step.

1. Calculate $2lw$: $$2lw=2\cdot 9\cdot 3=54{\text{ in}}^2$$

2. Calculate $2lh$: $$2lh=2\cdot 9\cdot 5=90{\text{ in}}^2$$

3. Calculate $2wh$: $$2wh=2\cdot 3\cdot 5=30{\text{ in}}^2$$

Now, sum these areas to find the total surface area:

$$\text{Surface Area}=2lw+2lh+2wh=54+90+30=174{\text{ in}}^2$$

Thus, the surface area of the rectangular prism is

$$\boxed{{\displaystyle 174}}{\text{ in}}^2$$