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.
L=Ph
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 5in and width 1in. Its perimeter is twice the sum of these two numbers.
P=2( 5+ 1) ⇔ P= 12in
We also know that the lateral area of the solid is 48in^2. With this information, we can find the height of the prism.
