Question

find the area of the given geometric figure. the area of the trapezoid is \boxed{} (simplify your answer.)

Explanation:

Step1: Recall trapezoid area formula

The formula for the area of a trapezoid is $A = \frac{1}{2}(b_1 + b_2)h$, where $b_1$ and $b_2$ are the lengths of the two parallel sides (bases), and $h$ is the height (the perpendicular distance between the bases).

Step2: Identify values from the figure

From the given trapezoid, $b_1 = 6\,\text{m}$, $b_2 = 8\,\text{m}$, and $h = 5\,\text{m}$.

Step3: Substitute values into the formula

Substitute $b_1 = 6$, $b_2 = 8$, and $h = 5$ into the formula:
\[

$$\begin{align*} A&=\frac{1}{2}(6 + 8)\times5\\ &=\frac{1}{2}(14)\times5\\ &= 7\times5\\ &= 35 \end{align*}$$

\]

Answer:

35 square meters