解：?$(2)$?設(shè)?$EF = x，$?
則?$CE = x，$??$DE = 4 - x，$??$AE = 4 + x。$?
在?$Rt\triangle ADE$?中，
∵?$DE^2+AD^2=AE^2，$?
∴?$(4 - x)^2+4^2=(4 + x)^2，$?
展開式子得：?$16 - 8x + x^2+16 = 16 + 8x + x^2，$?
移項可得：?$16 - 8x + x^2+16 - 16 - 8x - x^2=0，$?
合并同類項得：?$-16x + 16 = 0，$?
移項得：?$16x = 16，$?
?$ $?解得?$x = 1，$?
∴?$DE = 4 - 1 = 3，$?
∴?$S_{\triangle ADE}=\frac {1}{2}AD·DE=\frac {1}{2}×4×3 = 6 。$?
