?$ (1)$?證明：連接?$AC$?
在?$?AEC$?和?$?AF C$?中
?$ \begin {cases}{AE=AF}\\{CE=CF}\\{AC=AC}\end {cases}$?
∴?$?AEC≌?AF C(\mathrm {SSS})$?
∴?$∠EAC=∠F AC$?
∵?$CB⊥AB，$??$CD⊥AD，$?
∴?$∠ABC=∠ADC=90°$?
在?$?ABC$?和?$?ADC$?中
?$ \begin {cases}{∠BAC=∠DAC}\\{∠ABC=∠ADC}\\{AC=AC}\end {cases}$?
∴?$?ABC≌?ADC(\mathrm {AAS})$?
∴?$CB=CD$?
?$(2)$?解：∵?$AE=AF=8，$??$CD=CB=6$?
由?$(1)$?知?$?AEC≌?AF C$?
∴?$S_{四邊形AECF}=S_{△AEC}+S_{△AF} C=2×S_{△AEC}$?
?$=2×(\frac {1}{2}×AE×CB)=2×(\frac {1}{2}×8×6)=48$?
