Q9. - Algebra 1

Question

Find the surface area of each solid.

Step-by-Step Solution

Answer

The surface area of the rectangular prism is 108 square inches.

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.

It is clear, from the given figure, that the given solid is a rectangular prism of length 12 in., width 6 in. and height 2 in. 

Then, $l=12\mathrm{in}.$, $w=6\mathrm{in}.$ and $h=2\mathrm{in}.$

Step 3. Calculate the surface area.

Put $l=12$, $w=6$ and $h=2$ in $S=lw+wh+hl$ to get,

$$\begin{gathered} S=\left(12\right)\left(6\right)+\left(6\right)\left(2\right)+\left(2\right)\left(12\right) \\ =72+12+24 \\ =108 \end{gathered}$$

So, $S=108$.

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 108 square inches.