解：∵?$∠B = 90°，$??$AB = 3，$??$BC = 4$?
∴?$AC^2=AB^2+BC^2=25，$??$AC=5$?
?$ $?在?$\triangle ACD$?中，?$AC^2=25，$??$CD = 12，$??$AD = 13$?
∵?$AC^2+CD^2=25+12^2= 169，$??$AD^2=13^2=169$?
∴?$AC^2+CD^2=AD^2$?
∴?$\triangle ACD$?是直角三角形，且?$∠ACD = 90°$?
∴?$S_{四邊形ABCD}= S_{\triangle ABC}+S_{\triangle ACD}$?
?$ =\frac 12×AB×BC+\frac 12×AC×CD$?
?$ =\frac 12×3×4+\frac 12×5×12=36$?
