The correct option is C 13.5 cm2
By pythogoras theorem, AB2+BC2=AC2
⇒BC2=AC2−AB2
⇒BC2=152−92
⇒BC2=225−81=144
⇒BC=12 cm
As D and E are mid-points of AB and AC, by mid-point theorem, DE∥BC and DE=12BC=6 cm
Since, DE∥BC, we have ΔADE congruent to ΔABC
Area (ΔADE)Area (ΔABC)=DE2BC2
⇒Area (ΔADE)12×AB×BC=(6)2BC2
⇒Area (ΔADE)12×9×12=36144
⇒Area (ΔADE)=14×9×6
⇒Area (ΔADE)=274=13.5 cm2