Find the surface area of a rectangular prism prism (a box) if the dimensions are 4 m wide, 6 m long, and 3 m high

Question

UpStudy AI · Accepted Answer

To find the surface area of a rectangular prism (or box), you can use the formula:

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

where:
- $$ l $$ is the length,
- $$ w $$ is the width,
- $$ h $$ is the height.

Given the dimensions:
- Width ($$ w $$) = 4 m
- Length ($$ l $$) = 6 m
- Height ($$ h $$) = 3 m

Now, plug in the values:

$$
\text{Surface Area} = 2(6 \times 4 + 6 \times 3 + 4 \times 3)
$$

Calculating each term inside the parentheses:

1. $$ 6 \times 4 = 24 $$
2. $$ 6 \times 3 = 18 $$
3. $$ 4 \times 3 = 12 $$

Now, add these results together:

$$
24 + 18 + 12 = 54
$$

Now, multiply by 2:

$$
\text{Surface Area} = 2 \times 54 = 108 \, \text{m}^2
$$

Thus, the surface area of the rectangular prism is $$ \boxed{108} \, \text{m}^2 $$.
The surface area of the rectangular prism is 108 m².

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