Question

the area of the trapezoid is 22 square yards. what is the trapezoids height, h? h = yards

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, \(A = 22\) square yards, \(a=7\) yd, \(b = 4\) yd.

Step2: Substitute the values into the formula

Substitute into \(A=\frac{(a + b)h}{2}\), we get \(22=\frac{(7 + 4)h}{2}\).

Step3: Simplify the equation

First, simplify \(7 + 4=11\). The equation becomes \(22=\frac{11h}{2}\).

Step4: Solve for \(h\)

Multiply both sides of the equation by \(2\): \(22\times2=11h\), so \(44 = 11h\). Then divide both sides by \(11\): \(h=\frac{44}{11}\).

Answer:

\(4\)