1. The problem is to find the area of a trapezoid using the formula for the area of a trapezoid. 2. The formula for the area $A$ 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 bases, and $h$ is the height (the perpendicular distance between the bases). 3. From the problem, the two bases are $b_1 = 5$ m and $b_2 = 9$ m. 4. The height is given as $3.8$ m on the left side and $3.2$ m on the right side, but since the right side has a right angle, the height is the perpendicular distance between the bases, which is $3.2$ m. 5. Plugging the values into the formula: $$A = \frac{1}{2} (5 + 9) \times 3.2$$ 6. Simplify inside the parentheses: $$A = \frac{1}{2} \times 14 \times 3.2$$ 7. Multiply $\frac{1}{2} \times 14$: $$A = \cancel{\frac{1}{2}} \times \cancel{14} \times 3.2 = 7 \times 3.2$$ 8. Multiply $7 \times 3.2$: $$A = 22.4$$ 9. Therefore, the area of the trapezoid is $22.4$ square meters.