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. We know that the base is a rectangle with length 25cm and width 18cm. Its perimeter is twice the sum of these two numbers.
P=2( 25+ 18) ⇔ P= 86cm
We also know that the height of the solid is 12cm. With this information, we can find the lateral area of the prism.
We found that the lateral area of the prism is 1032cm^2. Note that the lateral area may change if we were to consider another dimension as the base.
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= 1032cm^2. Moreover, notice that the base is a rectangle with length 25cm and width 18cm. Therefore, to find its area, we will multiply these two numbers.
B= 25( 18) ⇔ B= 450cm^2
Now, we can substitute L= 1032 and B= 450 in the formula for the surface area, and simplify.
