Alexis ordered an ice cream cake from Molly Moo Creamery. The box that it was packed in was a rectangular prism. The dimensions of the box are shown in the diagram.

Question

7 in.

12.4 in.

9.1 in.

What is the total surface area of the box of in square inches?

Answer 1

To find the total surface area of a rectangular prism (box), 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.

In your case, the dimensions of the box are:

• Length ($l$) = 12.4 inches
• Width ($w$) = 7 inches
• Height ($h$) = 9.1 inches

Now, plug these dimensions into the formula:

1. Calculate $lw$: $$lw=12.4\times 7=86.8,\text{square inches}$$

2. Calculate $lh$: $$lh=12.4\times 9.1=113.84,\text{square inches}$$

3. Calculate $wh$: $$wh=7\times 9.1=63.7,\text{square inches}$$

4. Now add these areas together: $$lw+lh+wh=86.8+113.84+63.7=264.34,\text{square inches}$$

5. Finally, multiply by 2 to find the total surface area: $$\text{Surface Area}=2\times 264.34=528.68,\text{square inches}$$

So, the total surface area of the box is $\boxed{{\displaystyle 528.68}}$ square inches.