Question

what is the area of the trapezoid?
2 m
5 m
4 m
5 m
square meters

Explanation:

Step1: Recall the trapezoid area formula

The area of a trapezoid is given by \( A=\frac{(a + b)h}{2} \), where \( a \) and \( b \) are the lengths of the two parallel sides, and \( h \) is the height (the perpendicular distance between the parallel sides).
From the diagram, the two parallel sides (bases) are \( a = 2\space m \) and \( b = 5\space m \), and the height \( h = 4\space m \) (since it's the perpendicular side).

Step2: Substitute the values into the formula

Substitute \( a = 2 \), \( b = 5 \), and \( h = 4 \) into the formula:
\[

$$\begin{align*} A&=\frac{(2 + 5)\times4}{2}\\ &=\frac{7\times4}{2}\\ &=\frac{28}{2}\\ &= 14 \end{align*}$$

\]

Answer:

The area of the trapezoid is \(\boldsymbol{14}\) square meters.