Question

Find the surface area of each rectangular prism given the measurements below.

$l=6\mathrm{in}.,w=1\mathrm{in}.,h=4\mathrm{in}.$

Short answer

The surface area of the rectangular prism is 34 square inches.

Step-by-step solution

Step 1. State the formula.

The formula for surface area of a rectangular prism is $S=lw+wh+hl$, where S is the surface area, l is the length, w is the width and h is the height of the rectangular prism.

Step 2. List the given data.

$l=6\mathrm{in}.$, $w=1\mathrm{in}.$and$h=4\mathrm{in}.$

Step 3. Calculate the surface area.

Put $l=6$, $w=1$and $h=4$in $S=lw+wh+hl$to get,

$$\begin{gathered} S=\left(6\right)\left(1\right)+\left(1\right)\left(4\right)+\left(4\right)\left(6\right) \\ =6+4+24 \\ =34 \end{gathered}$$

So, $S=34$.

Step 4. Determine the unit.

Since the unit of length, width and height are all given as inches, the unit of the surface area must be square inches.

So, the surface area of the rectangular prism is 34 square inches.