1. **State the problem:** Find the area of the trapezoid with top base 7 m, height 6 m, and bottom base composed of two segments 5 m and 2 m. 2. **Formula for the area of a trapezoid:** $$\text{Area} = \frac{(b_1 + b_2)}{2} \times h$$ where $b_1$ and $b_2$ are the lengths of the two parallel bases, and $h$ is the height. 3. **Identify the bases and height:** - Top base $b_1 = 7$ m - Bottom base $b_2 = 5 + 2 = 7$ m (sum of left and right bottom extensions) - Height $h = 6$ m 4. **Calculate the area:** $$\text{Area} = \frac{(7 + 7)}{2} \times 6 = \frac{14}{2} \times 6$$ 5. **Simplify the fraction:** $$= \cancel{\frac{14}{2}} \times 6 = 7 \times 6$$ 6. **Multiply to find the area:** $$= 42$$ 7. **Conclusion:** The area of the trapezoid is 42 square meters. Note: The given 75 m² does not match the calculated area based on the provided dimensions, so the correct area based on the given measurements is 42 m².