Question

find the area of the trapezoid. the trapezoid has an area of m².

Explanation:

Step1: Recall the area formula of trapezoid

The formula for the area 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.

Step2: Identify the values of \(a\), \(b\), and \(h\)

From the figure, \(a = 4m\), \(b=8m\), and \(h = 6m\).

Step3: Substitute the values into the formula

Substitute \(a = 4\), \(b = 8\), and \(h = 6\) into \(A=\frac{(a + b)h}{2}\), we get \(A=\frac{(4 + 8)\times6}{2}\).
First, calculate the sum of the parallel sides: \(4+8=12\). Then multiply by the height: \(12\times6 = 72\). Finally, divide by 2: \(\frac{72}{2}=36\).

Answer:

\(36\)