Which of the following can be used to find the surface area, in square inches, of a rectangular prism with length 36 inches, width 18 inches, and height 18 inches?

Understand the Problem

The question describes a rectangular prism (box) and asks which expression correctly calculates its surface area. We need to determine the dimensions of the box (length, width, height) from the description and then identify the formula for the surface area of a rectangular prism that uses those dimensions correctly.

Answer

$2(lw + lh + wh)$

Steps to Solve

Recall the surface area formula

The surface area of a rectangular prism is the sum of the areas of all its faces. A rectangular prism has 6 faces, where opposite faces have equal areas.

Calculate the area of each pair of faces
- Two faces have area length $\times$ width: $lw$. So, the combined area is $2lw$.
- Two faces have area length $\times$ height: $lh$. So, the combined area is $2lh$.
- Two faces have area width $\times$ height: $wh$. So, the combined area is $2wh$.
Sum the areas of all faces

Adding the areas of all six faces gives the total surface area: $2lw + 2lh + 2wh$.
Factor out the 2

The surface area can be written as $2(lw + lh + wh)$.

The expression that represents the surface area of a rectangular prism with length $l$, width $w$, and height $h$ is:

$2(lw + lh + wh)$

More Information

The surface area represents the total area you would need to cover the outside of the rectangular prism. Think of it as the amount of wrapping paper needed to wrap a box.

Tips

A common mistake is to forget to account for all six faces of the rectangular prism. Remembering that each pair of opposite faces contributes $2lw$, $2lh$, and $2wh$ to the total surface area can help avoid this error. Another mistake is not distributing the 2 correctly if the formula is presented in the factored form.

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