Question

the area of the trapezoid is 27 square centimeters. what is the trapezoids height, h? h = centimeters

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, \(A = 27\space cm^{2}\), \(a=5\space cm\), \(b = 13\space cm\).

Step2: Substitute values into the formula

Substitute the values into the formula: \(27=\frac{(5 + 13)h}{2}\).
First, simplify the sum of the parallel sides: \(5+13 = 18\). So the equation becomes \(27=\frac{18h}{2}\).
Since \(\frac{18h}{2}=9h\), the equation is \(27 = 9h\).

Step3: Solve for \(h\)

Divide both sides of the equation \(27 = 9h\) by \(9\). \(\frac{27}{9}=h\).

Answer:

\(3\)