\[\begin{array}{l} MF = h \hfill \\ CK = 2h \hfill \\ {S_{AMD}} = {S_{ECD}} = 2h \hfill \\ {S_{ABCD}} = \frac{7}{2} \cdot 2h = 7h \hfill \\ {\text{а)}} \hfill \\ {S_{AMOE}} = {S_{AMD}} - {S_{EOD}} = 2h - {S_{EOD}} \hfill \\ {S_{COD}} = {S_{ECD}} - {S_{EOD}} = 2h - {S_{EOD}} = {S_{AMOE}} \hfill \\ {\text{б)}} \hfill \\ {\text{Пусть }}N{\text{ - середина }}CE.{\text{ Тогда }}MN{\text{ - средняя линия трапеции }}ABCE. \hfill \\ MN = \frac{{BC + AE}}{2} = \frac{5}{2}. \hfill \\ PH \bot MN,{\text{ }}O \in PH. \hfill \\ \frac{{OH}}{{OP}} = \frac{2}{{\frac{5}{2}}} \Leftrightarrow OP = \frac{5}{4}OH \hfill \\ OH + \frac{5}{4}OH = h \Leftrightarrow OH = \frac{4}{9}h \hfill \\ {S_{EOD}} = \frac{1}{2} \cdot ED \cdot OH = \frac{4}{9}h \hfill \\ {S_{AMOE}} = {S_{AMD}} - {S_{EOD}} = 2h - \frac{4}{9}h = \frac{{14}}{9}h \hfill \\ \frac{{{S_{AMOE}}}}{{{S_{ABCD}}}} = \frac{{\frac{{14}}{9}h}}{{7h}} = \frac{2}{9}. \hfill \\ \end{array}\]

\[{\text{б) }}\frac{2}{9}\]