Exercise 2 Page 849

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. 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 $11\text{ m}$ and width $10\text{ m}.$ Its perimeter is twice the sum of these two numbers. We also see in the diagram that the height of the solid is $15\text{ m}.$ With this information, we can find the lateral area of the prism. We found that the lateral area of the prism is $630{\text{ m}}^2.$

Surface Area

Let's now recall the formula for the surface area of a prism $S.$ Here, $L$ is the lateral area and $B$ is the area of the base. Note that we already know that $L=630{\text{ m}}^2.$ Moreover, notice that the base is a rectangle with length $11\text{ m}$ and width $10\text{ m}.$ Therefore, to find its area, we will multiply these two numbers. Now, we can substitute $L=630$ and $B=110$ in the formula for the surface area, and simplify. The surface area of the prism is $850{\text{ m}}^2.$