Exercise 11 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 rectangle with length 6in and width 2in. Its perimeter is twice the sum of these two numbers. P=2( 6+ 2) ⇔ P= 16in We also see in the diagram that the height of the solid is 4m. With this information, we can find the lateral area of the prism.

L=Ph

SubstituteII

P= 16, h= 4

L= 16( 4)

Multiply

Multiply

L=64

Therefore, the lateral area of the solid is 64 in^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= 64in^2. Moreover, notice that the base is a rectangle with length 6in and width 2in. Therefore, to find its area, we will multiply these two numbers. B= 6( 2) ⇔ B= 12in^2 Now, we can substitute L= 64 and B= 12 in the formula for the surface area, and simplify.

S=L+2B

SubstituteII

L= 64, B= 12

S= 64+2( 12)

▼

Evaluate right-hand side

Multiply

Multiply

S=64+24

AddTerms

Add terms

S=88

The surface area of the prism is 88 in^2.