Exercise 9 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 right triangle. We see in the diagram that the lengths of the legs of this triangle are 4ft and 3ft. We can find the hypotenuse by using the Pythagorean Theorem.

Now we know the lengths of the three sides of the base. Let's add them to find its perimeter. P&= 5+ 4+ 3 P&= 12ft We will now substitute P= 12 and h= 2 in the formula for the lateral area of a prism.

The lateral area of the solid is 24 ft^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=24ft^2. We can calculate the area of the base using the formula for area of a triangle.

The area of the base is 6ft^2. Now we have enough information to find the surface area of the prism. Let's substitute 24 and 6 for L and B, respectively, into the corresponding formula.

The surface area of the prism is 36ft^2.