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 square, this means that the length of each base side is 1.5mm. Its perimeter is four times this number.
P=4( 1.5) ⇔ P= 6mm
We also see in the diagram that the height of the solid is 1.5mm. With this information, we can find the lateral area of the prism.
We found that the lateral area of the prism is 9mm^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= 9mm^2. Moreover, notice that the base is a square with side length of 1.5mm. Therefore, we can find the area by squaring this number.
B= 1.5^2 ⇔ B= 2.25mm^2
Now, we can substitute L= 9 and B= 2.25 in the formula for the surface area, and simplify.
