The formula for the area of a trapezoid is

A =
h(B + b)
2
.
The area of the truss is 20 square feet. Find the height of the truss if the shorter base is the same as the height h.

so

20=1/2 *h(h+B)

cant be solved without the longer base given.

sorry the longer base is 18

Then put 18 in for B, and solve. Note it is quadratic equation, put it in standard form

ax^2 + bx +c=0
and use the quadratic equation

To find the height of the truss, we need to rearrange the formula for the area of a trapezoid and solve for h.

The formula for the area of a trapezoid is given as:
A = (h*(B + b))/2

Given that the area of the truss is 20 square feet, we can substitute this value into the formula:
20 = (h*(B + b))/2

Now, we know that the shorter base is the same as the height h. Let's denote the shorter base as b and the longer base as B. Since b is equal to h, we can substitute h for b:
20 = (h*(B + h))/2

To simplify the equation, we can distribute the h inside the parentheses:
20 = (h*B + h^2)/2

Next, we can multiply both sides of the equation by 2 to eliminate the fraction:
40 = h*B + h^2

Rearranging the terms:
h^2 + h*B - 40 = 0

Now, we have a quadratic equation. To solve it, we can either factor it or use the quadratic formula. In this case, let's use the quadratic formula:
h = (-B ± √(B^2 - 4*a*c)) / (2*a)

In the equation h^2 + h*B - 40 = 0, we can identify a = 1, b = B, and c = -40. Substituting these values into the quadratic formula, we get:
h = (-B ± √(B^2 - 4*1*(-40))) / (2*1)

Simplifying further, we have:
h = (-B ± √(B^2 + 160)) / 2

This gives us two possible values for h, which will depend on the values of B. Plug in the appropriate values for B, and solve for h using the quadratic formula.