Calculate area of KDE contours in Python

Question

So I've done a KDE in python via the following:

y = coords[:,1]   ## A set of y coordinates of the red points
x = coords[:,0]   ## A set of x coordinates of the red points
k = gaussian_kde(np.vstack([x, y]))
k.set_bandwidth(bw_method=k.factor / 2.)

xi, yi = np.mgrid[x.min():x.max():x.size**0.8*1j,y.min():y.max():y.size**0.8*1j]
zi = k(np.vstack([xi.flatten(), yi.flatten()]))

fig, ax = plt.subplots(1, 1, figsize=(16, 8))

for coord in coordsold:
  cv2.circle(sample,
           (coord[1],coord[0]),2,
            (220, 0, 0), 1)

ax.contourf(yi, xi, zi.reshape(xi.shape), alpha=0.5)
    
ax.set_axis_off()
ax.imshow(sample)

What I want to figure out is the area that the contours take up. I thought that maybe I could turn the contours into polygon objects and then calculate the area that way, but I'm not sure. If anyone has a clever solution that would be greatly appreciated.

See attached: