ВН – высота. \(BC = 14,\,\,\,\,\,AD = 26,\,\,\,\,\,\,AB = CD.\)
\(p = BC + AD + 2 \cdot AB = 60\)
\(14 + 26 + 2 \cdot AB = 60\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,AB = 10.\)
\(AH = \frac{{AD — BC}}{2} = \frac{{26 — 14}}{2} = 6.\)
По теореме Пифагора из треугольника АВН:
\(A{B^2} = A{H^2} + B{H^2}\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,B{H^2} = {10^2} — {6^2} = 64\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\,BH = 8.\)
Тогда: \(S = \frac{{AD + BC}}{2} \cdot BH = \frac{{14 + 26}}{2} \cdot 8 = 160.\)
Ответ: 160.