Let's analyze the solid that represents a barn. We rotate it to better see the bases of the prism.
The height of the prism is h=36 feet. Let's analyze the base.
Unfortunately, we do not know if any of the sides are perpendicular or not. We assume that they are perpendicular. Otherwise, we have too little data to solve this exercise.
Now, let's find the area of the base in terms of x. First, let's divide the base into two parts — a rectangle and a right triangle.
Since the rectangle has sides 8 and 18 feet, its area is 8* 18=144 square feet. The right triangle has legs x and x. Therefore, its area is 12(x)(x)= 12x^2. This tells us that the area of the base, B, is the sum of these two areas.
Area of the base:
B=144+1/2x^2
We know that the volume of the solid is 9072 cubic feet. By the formula for the volume of a prism, V=Bh, we can get an equation with x. We will write that equation and solve it for x.
