Exercise 12 Page 818

We are asked to find the lateral area and surface area of the given prism.

Let's do these things one at a time.

Lateral Area

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.

L=Ph

SubstituteII

P= 6, h= 1.5

L= 6( 1.5)

Multiply

Multiply

L=9

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.

S=L+2B

SubstituteII

L= 9, B= 2.25

S= 9+2( 2.25)

▼

Evaluate right-hand side

Multiply

Multiply

S=9+4.5

AddTerms

Add terms

S=13.5

The surface area of the prism is 13.5 mm^2.