Find the surface area of this rectangular prism. Be sure to include the correct unit in your answer.

Understand the Problem

The question asks to calculate the surface area of a rectangular prism with given dimensions (length, width, and height). The surface area can be found using the formula SA = 2(lw + lh + wh), where l is length, w is width, and h is height.

Answer

The surface area is $ 232 \, \text{m}^2 $.

Steps to Solve

Identify the dimensions of the prism

The dimensions given for the rectangular prism are:

Length ($l$) = 8 m
Width ($w$) = 4 m
Height ($h$) = 7 m

Apply the surface area formula

Use the surface area formula for a rectangular prism: $$ SA = 2(lw + lh + wh) $$

Calculate the individual area components

Calculate each component within the formula:

First, calculate $lw$: $$ lw = 8 , \text{m} \times 4 , \text{m} = 32 , \text{m}^2 $$
Next, calculate $lh$: $$ lh = 8 , \text{m} \times 7 , \text{m} = 56 , \text{m}^2 $$
Finally, calculate $wh$: $$ wh = 4 , \text{m} \times 7 , \text{m} = 28 , \text{m}^2 $$

Sum the area components

Add the three components together: $$ lw + lh + wh = 32 , \text{m}^2 + 56 , \text{m}^2 + 28 , \text{m}^2 = 116 , \text{m}^2 $$

Calculate the total surface area

Multiply the sum by 2 to find the total surface area: $$ SA = 2(116 , \text{m}^2) = 232 , \text{m}^2 $$

The surface area of the rectangular prism is ( 232 , \text{m}^2 ).

More Information

The surface area of a rectangular prism is important in real-world applications, such as packaging, construction, and materials estimation. Understanding how to calculate it helps in assessing how much material is needed for surfaces.

Tips

Confusing length, width, and height can lead to incorrect calculations. Ensure to clearly label and use the correct dimensions.
Forgetting to multiply the summed areas by 2 for the total surface area. Always remember this final step.

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