So i have been given a practical for a non-hookean material i.e. polymer, we were to add weights progressively and then taking them off one by one. After doing so i plotted the weight attached to the polymer vs the length stretched for both adding and removing the weights on the same graph. The teacher told us the area inbetween the two curves is the energy lost/work done and and approximation of the spring constant are the tangents at which the graph curves, such that there are six tangents in total. But i don't understand why the area inbetween the two curves is the energy lost/work done and why the tangents at which the graph curve are approximations of the spring constant?? Please help!