Drooping Octagon

Consider a regular octagon consisting of 8 point masses and 11 springs. 8 of the springs are arranged in a sequential chain around the perimeter, as shown in the first diagram below. The other 3 are horizontal support springs (also as shown in the first diagram).

The springs all have a force constant of $20 \, \text{N/m}$ , and all springs are at their natural lengths in the first diagram (clearly, not all the natural lengths are the same). Gravity is $10 \, \text{m/s}^2$ downward. The highest (farthest upward) mass is fixed in place and cannot move. All other masses can move.

At time $t = 0$ , the masses have the following properties (all quantities in SI units): $\begin{aligned} \text{subscript}:\ &k = 0\sim 7 \\ \text{Mass}:\ &m_k = 1 \\ \text{xpos}:\ &x_k = \cos(\pi/2 - k \pi/4) \\ \text{ypos}:\ &y_k = \sin(\pi/2 - k \pi/4) \\ \text{xvel}:\ &\dot{x}_k = 0 \\ \text{yvel}:\ &\dot{y}_k = 0. \end{aligned}$ The system moves over time until it eventually reaches stasis due to the effects of air resistance. The shape begins as a regular octagon and ends as an irregular octagon (see the second figure).

What is the ratio of the final irregular octagon area to the initial regular octagon area?

Initial State (to-scale):

Final State (not-to-scale):