ВН – высота. \(AD = 18,\,\,\,\,\,BC = 6,\,\,\,\,\,\,AB = 7,\,\,\,\,\,\,\angle \,ABC = {150^ \circ }.\)
\(\angle \,A = {180^ \circ } — \angle \,ABC = {180^ \circ } — {150^ \circ } = {30^ \circ }.\)
По определению синуса из треугольника АВН:
\(\sin A = \frac{{BH}}{{AB}}\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\sin {30^ \circ } = \frac{{BH}}{7}\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,\,\frac{1}{2} = \frac{{BH}}{7}\,\,\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,BH = \frac{7}{2}.\)
Тогда: \({S_{ABCD}} = \frac{{BC + AD}}{2} \cdot BH = \frac{{6 + 18}}{2} \cdot \frac{7}{2} = 42.\)
Ответ: 42.