\[\boxed{\mathbf{569\ (569)}.\ Еуроки\ - \ ДЗ\ без\ мороки}\]
\(P = 162\ дм;\ \ a = 47\ дм:\)
\[P = 2 \cdot (a + b) = 2 \cdot (47 + b) =\]
\[= 162\]
\[47 + b = 162\ :2\]
\[b = 81 - 47 = 34\ (дм) -\]
\[ширина.\]
\[S = a \cdot b = 47 \cdot 34 = 1598\ дм^{2}.\]
\[Ответ:1598\ дм^{2}.\]