Question

applying the area of a trapezoid formula
a plot of land has an area of 33.75 square feet. jackson wants to put a 4 - foot by 4 - foot shed on the land. he can only do this if the height of the trapezoid is at least 4.5 feet. what is the height of the trapezoid?
feet

Explanation:

Step1: Recall the area formula of a trapezoid

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, \(a = 5\) ft, \(b=10\) ft, and \(A = 33.75\) square feet.

Step2: Substitute the values into the formula

Substitute \(A = 33.75\), \(a = 5\), and \(b = 10\) into \(A=\frac{(a + b)h}{2}\), we get \(33.75=\frac{(5 + 10)h}{2}\).

Step3: Simplify the equation

First, simplify the denominator: \(\frac{(5 + 10)h}{2}=\frac{15h}{2}\). So the equation becomes \(33.75=\frac{15h}{2}\).

Step4: Solve for \(h\)

Multiply both sides of the equation by \(2\): \(33.75\times2=15h\), which is \(67.5 = 15h\). Then divide both sides by \(15\): \(h=\frac{67.5}{15}=4.5\)

Answer:

\(4.5\)