Exercise 2 Page 817

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. Let's start by finding the perimeter of the base. In the diagram, we see that the base is a rectangle with length 11m and width 10m. Its perimeter is twice the sum of these two numbers. P=2( 11+ 10) ⇔ P= 42m We also see in the diagram that the height of the solid is 15m. With this information, we can find the lateral area of the prism.

L=Ph

SubstituteII

P= 42, h= 15

L= 42( 15)

Multiply

Multiply

L=630

We found that the lateral area of the prism is 630m^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= 630m^2. Moreover, notice that the base is a rectangle with length 11m and width 10m. Therefore, to find its area, we will multiply these two numbers. B= 11( 10) ⇔ B= 110m^2 Now, we can substitute L= 630 and B= 110 in the formula for the surface area, and simplify.

S=L+2B

SubstituteII

L= 630, B= 110

S= 630+2( 110)

▼

Evaluate right-hand side

Multiply

Multiply

S=630+220

AddTerms

Add terms

S=850

The surface area of the prism is 850 m^2.