Facial Expression Recognition (FER) has many real life applications in Human-Computer Interaction (HCI). The detection of basic facial expressions such as Anger, Disgust, Fear, Happiness, Sadness, and Surprise in a given face image is a challenging problem. The authors propose a novel method where 1) The Active Appearance Model (AAM) is used to generate sixty-eight facial landmark points. 2) Then twenty salient landmark points out of sixty-eight points are identified and used to form triangulation on the face. 3) Then seven different geometric shape factors are calculated for each triangle in the triangulation set. 4) Each of their shape factors is trained with Multi-Layer Perceptron (MLP) for the classification of expressions. 5) Then the best performing shape factor is selected as the final feature. The proposed method is well tested on benchmark databases viz. CK+, JAFFE, MMI, and MUG. The effective and efficient learning of the shape factor with MLP shows extremely encouraging results.