Question

the area of the trapezoid is 450 square feet. what is the trapezoids height, h? h = feet

Explanation:

Step1: Recall the trapezoid area formula

The area formula of a trapezoid is \(A=\frac{(a + b)h}{2}\), where \(a\) and \(b\) are the lengths of the parallel sides, and \(h\) is the height. Here, \(A = 450\) square feet, \(a=18\) feet, \(b = 12\) feet.

Step2: Substitute the values into the formula

Substitute \(A = 450\), \(a = 18\), \(b=12\) into \(A=\frac{(a + b)h}{2}\), we get \(450=\frac{(18 + 12)h}{2}\).

Step3: Simplify the equation

First, simplify the sum of the parallel sides: \(18+12 = 30\). The equation becomes \(450=\frac{30h}{2}\). Since \(\frac{30h}{2}=15h\), the equation is \(15h=450\).

Step4: Solve for \(h\)

Divide both sides of the equation \(15h = 450\) by \(15\). So, \(h=\frac{450}{15}\).

Answer:

\(h = 30\) feet