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 6in and width 2in. Its perimeter is twice the sum of these two numbers.
P=2( 6+ 2) ⇔ P= 16in
We also see in the diagram that the height of the solid is 4m. With this information, we can find the lateral area of the prism.
Therefore, the lateral area of the solid is 64 in^2.
Surface Area
Let's now recall the formula for the surface area of a prism S.
S=L+2B
Here, L is the lateral area and B is the area of the base. Note that we already know that L= 64in^2. Moreover, notice that the base is a rectangle with length 6in and width 2in. Therefore, to find its area, we will multiply these two numbers.
B= 6( 2) ⇔ B= 12in^2
Now, we can substitute L= 64 and B= 12 in the formula for the surface area, and simplify.
