Answer
$$163{\text{ k}}{{\text{m}}^2}$$
Work Step by Step
$$\eqalign{
& C = {\text{142}}.{\text{7}}^\circ ,a = {\text{21}}.{\text{9 km}},b = {\text{24}}.{\text{6 km}} \cr
& {\text{Find the area of the triangle using the formula }}A = \frac{1}{2}ab\sin C \cr
& A = \frac{1}{2}\left( {{\text{21}}.{\text{9 km}}} \right)\left( {{\text{24}}.{\text{6 km}}} \right)\sin \left( {{\text{142}}.{\text{7}}^\circ } \right) \cr
& {\text{Using a calculator}} \cr
& A \approx 163{\text{ k}}{{\text{m}}^2} \cr} $$
