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 = P h

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

1.5 mm .

Its perimeter is four times this number.

P = 4 (1.5) \Leftrightarrow P = 6 mm

We also see in the diagram that the height of the solid is

1.5 mm .

With this information, we can find the lateral area of the prism.

L = P h

SubstituteII

$P = 6$ , $h = 1.5$

L = 6 (1.5)

Multiply

L = 9

We found that the lateral area of the prism is

9 mm^{2} .

Surface Area

Let's now recall the formula for the surface area of a prism

S .

S = L + 2 B

Here,

L

is the lateral area and

B

is the area of the base. Note that we already know that

L = 9 mm^{2} .

Moreover, notice that the base is a square with side length of

1.5 mm .

Therefore, we can find the area by squaring this number.

B = 1.5^{2} \Leftrightarrow B = 2.25 mm^{2}

Now, we can substitute

L = 9

and

B = 2.25

in the formula for the surface area, and simplify.

S = L + 2 B

SubstituteII

$L = 9$ , $B = 2.25$

S = 9 + 2 (2.25)

▼

Evaluate right-hand side

Multiply

S = 9 + 4.5

AddTerms

Add terms

S = 13.5

The surface area of the prism is

13.5 mm^{2} .

Exercise