\[\boxed{\mathbf{572\ (572)}.\ Еуроки\ - \ ДЗ\ без\ мороки}\]
\[P_{пр} = 4\ м\ 8\ дм = 48\ дм;\ \ a = 5b\]
\[P_{пр} = 2 \cdot (a + b) = 48\ дм.\]
\[5b + b = 48\ :2\]
\[6b = 24\]
\[b = 4\ дм.\]
\[a = 5b = 5 \cdot 4 = 20\ дм.\]
\[S = a \cdot b = 20 \cdot 4 = 80\ дм^{2}.\]
\[Ответ:80\ дм^{2}.\]