Several models have been proposed to describe the dynamics of epithelial tissues undergoing morphogenetic changes driven by apical constriction pulses, which differ in where the constriction is applied, either at the perimeter or medial regions. To help discriminate between these models, using the vertex model for epithelial dynamics, we analysed the impact of where the constriction is applied on the final geometry of the active cell that is reducing its apical size. We find that medial activity, characterised by a reduction in the reference area in the vertex model, induces symmetry breaking and generates anisotropic cell shapes, while isotropic cell shapes and larger contractions occur when the reference perimeter in the model is reduced. When plasticity is included, sufficiently slow processes of medial contractile activity, compared with typical apical constriction pulses, can also achieve significant cell contraction. Finally, we apply the model to describe the active apical contractile pulses observed during cellular mitotic events within the epithelial enveloping cell layer in the developing annual killifish Austrolebias nigripinnis, being able to quantitatively describe the temporal evolution of cell shape changes when perimeter activity and area plasticity are included. A global fit of all parameters of the vertex model is provided.