1. **State the problem:** Find the area of a trapezoid with top base $2$ km, height $2 \frac{1}{2}$ km, and bottom base $4 \frac{1}{3}$ km. 2. **Formula for the area of a trapezoid:** $$\text{Area} = \frac{(\text{base}_1 + \text{base}_2)}{2} \times \text{height}$$ 3. **Convert mixed numbers to improper fractions:** - Height: $2 \frac{1}{2} = \frac{5}{2}$ km - Bottom base: $4 \frac{1}{3} = \frac{13}{3}$ km 4. **Substitute values into the formula:** $$\text{Area} = \frac{(2 + \frac{13}{3})}{2} \times \frac{5}{2}$$ 5. **Find common denominator and add bases:** $$2 = \frac{6}{3}$$ $$2 + \frac{13}{3} = \frac{6}{3} + \frac{13}{3} = \frac{19}{3}$$ 6. **Simplify the fraction for the average of the bases:** $$\frac{\frac{19}{3}}{2} = \frac{19}{3} \times \frac{1}{2} = \frac{19}{6}$$ 7. **Calculate the area:** $$\text{Area} = \frac{19}{6} \times \frac{5}{2} = \frac{19 \times 5}{6 \times 2} = \frac{95}{12}$$ 8. **Convert to mixed number:** $$\frac{95}{12} = 7 \frac{11}{12}$$ **Final answer:** The area of the trapezoid is $7 \frac{11}{12}$ square kilometers.