To find the height of the truss in the given illustration, we can use the formula for the area of a trapezoid:
A = (h * (B + b)) / 2
Where A is the area, h is the height, B is the longer base, and b is the shorter base.
In this case, we are given that the area of the trapezoid truss is 72 square feet, and the shorter base is equal to the height.
Let's substitute the given values into the formula:
72 = (h * ((B + h)) / 2
Since we are told that the shorter base is the same as the height, we can substitute b with h:
72 = (h * ((B + h) / 2))
To solve this equation and find the height, we need to know the value of the longer base (B). Without that information, it is not possible to calculate the height of the truss.