解：?$(1)AD=\sqrt {AC^2-CD^2}=\sqrt {13^2-12^2}=5\ \mathrm {cm}$?
?$BC=\sqrt {BD^2+CD^2}=\sqrt {9^2+12^2}=15\ \mathrm {cm}$?
?$AB=AD+BD=5+9=14\ \mathrm {cm}$?
?$C_{△ABC}=AB+BC+AC=14+15+13=42\ \mathrm {cm}$?
∵?$DE//BC $?
∴?$△ADE∽△ABC$?
∴?$\frac {C_{△ADE}}{C_{△ABC}}=\frac {AD}{AB}=\frac 5{14}$?
∴?$C_{△ADE}=42×\frac 5{14}=15\ \mathrm {cm}$?
?$(2)S_{△ABC}=\frac 12AB ·CD=\frac 12×14×12=84\ \mathrm {cm^2}$?
?$\frac {S_{△ADE}}{S_{△ABC}}=(\frac 5{14})^2$?
∴?$S_{△ADE}=84×(\frac 5{14})^2=\frac {75}7\ \mathrm {cm^2}$?
