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. Let's start by finding the perimeter of the base. In the diagram, we see that the base is a rectangle with length 11m and width 10m. Its perimeter is twice the sum of these two numbers.
P=2( 11+ 10) ⇔ P= 42m
We also see in the diagram that the height of the solid is 15m. With this information, we can find the lateral area of the prism.
We found that the lateral area of the prism is 630m^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= 630m^2. Moreover, notice that the base is a rectangle with length 11m and width 10m. Therefore, to find its area, we will multiply these two numbers.
B= 11( 10) ⇔ B= 110m^2
Now, we can substitute L= 630 and B= 110 in the formula for the surface area, and simplify.
