1. **State the problem:** We have trapezoid JKMN with area 136 square km. The base KM is 20 km, and the height (distance from KM to JN) is 8 km. We need to find the area of triangle JKN formed by points J, K, and N. 2. **Recall the trapezoid area formula:** $$\text{Area} = \frac{(\text{sum of parallel sides}) \times \text{height}}{2}$$ Here, KM and JN are parallel sides. 3. **Calculate the length of JN:** Let the length of JN be $x$ km. Using the area formula: $$136 = \frac{(20 + x) \times 8}{2}$$ 4. **Simplify the equation:** $$136 = 4(20 + x)$$ Divide both sides by 4: $$\cancel{4} \times 34 = \cancel{4} (20 + x)$$ $$34 = 20 + x$$ 5. **Solve for $x$:** $$x = 34 - 20 = 14$$ So, the length of JN is 14 km. 6. **Find the area of triangle JKN:** Triangle JKN shares the height of 8 km (distance from KM to JN) and base KN. Since KM = 20 km and JN = 14 km, and trapezoid is formed by J, K, M, N in order, segment KN is the difference between KM and JN: $$KN = 20 - 14 = 6$$ 7. **Calculate area of triangle JKN:** $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 8 = 24$$ **Final answer:** The area of triangle JKN is $24$ square kilometres.