We are asked to find the height of the given prism.
The lateral area L of a prism is the sum of the areas of the lateral faces. Let's recall the formula for the lateral area of a prism.
\begin{gathered}
L=Ph
\end{gathered}
In this formula, $P$ is the perimeter of the base and $h$ the height of the prism. We will start by finding the perimeter of the base. In the diagram, we see that the base is a rectangle with length $\colV{5\text{ in}}$ and width $\colVI{1\text{ in}}.$ Its perimeter is twice the sum of these two numbers.
\begin{gathered}
P=2(\colV{5}+\colVI{1}) \quad \Leftrightarrow \quad P=\colII{12\text{ in}}
\end{gathered}
We also know that the lateral area of the solid is $\col{48\text{ in}^2}.$ With this information, we can find the height of the prism.
