Exercise 13 Page 818

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

We will do these things one at a time.

Lateral area

Let's recall the formula for the lateral area L of a prism. L=Ph Here, P is the perimeter of the base, and h the height of the prism. Note that the base is a triangle. We see in the diagram that the lengths of the legs of this triangle are 2.4m, 1.5m and 1.7 m. Let's add them to find its perimeter. P&= 2.4+ 1.5+ 1.7 P&= 5.6m Let's now substitute P= 5.6 and h= 2 in the formula for the lateral area of a prism.

The lateral area of the solid is 11.2 m^2.

Surface Area

Let's recall the formula for the surface area of a prism. S=L+2B Here, L is the lateral area of the prism and B the area of the base. We already know that L=11.2m^2. We can calculate the area of the base using the formula for area of a triangle.

The area of the base is 1.2m^2. Now we have enough information to find the surface area of the prism. Let's substitute 11.2 and 1.2 for L and B, respectively, into the corresponding formula and simplify.

The surface area of the prism is 13.6m^2.