Question

The surface area of a rectangular prism is 352 mm2. Two of the dimension are 4mm and 8mm. Find the measure of the other dimension.

Answer 1

Suppose this is your rectangular prism:

Suppose length is given as 8 mm, width given as 4 mm.

We need to find the height.

Let's look at the formula for surface area of rectangular prism:

$SA=2lw+2wh+2lh$

Where

l is length

w is width

h is height

Let's put the given dimensions in the formula:

$\begin{gathered} SA=2lw+2wh+2lh \\ SA=2(8)(4)+2(4)h+2(8)h \end{gathered}$

We are given SA = 352, we substitute, do algebra, and solve for h:

$\begin{gathered} SA=2(8)(4)+2(4)h+2(8)h \\ 352=64+8h+16h \\ 352=64+24h \\ 24h=352-64 \\ 24h=288 \\ h=\frac{288}{24} \\ h=12 \end{gathered}$

So the other dimension is 12 mm