Exercise 46 Page 847

The volume of a prism can be calculated using the following formula. In this formula B is the base area, and h is the height of a prism. V=Bh In our exercise the base is an isosceles triangle. Before we can evalaute the base area we need to find the height of the triangle. Note that in isosceles triangles the height bisects the base of a triangle.

Let's use the Pythagorean Theorem to calculate the value of h.

Note that, when solving the above equation, we only needed to consider the principal root because h is a positive number. Now we can calculate the base area of the prism. To do this let's use the formula for area of a triangle.

We found that the base area is 60ft^2. We are also given that the height equals 19ft. Let's substitute these values into the volume formula.

The volume of the prism is 1140ft^3.