$S_{△BEF}+S_{梯形ABDF}=S_{△ADE}$
$S_{△FCD}+S_{梯形ABDF}=S_{正方形ABCD}$
$S_{△BEF}-S_{△FCD}=80\ \mathrm {cm}^2$
$则S_{△ADE}-S_{正方形ABCD}=80\ \mathrm {cm}^2$
$S_{△ADE}=S_{正方形ABCD}+80=20×20+80=480(\mathrm {cm}^2)$
$480×2÷20=48(\mathrm {cm})$
$48-20=28(\mathrm {cm})$
$答：线段BE的长为28厘米.$
