1. Three of the four midpoints form a right triangle with the length of the hypotenuse of 2. Thus the distance between twoo midpoints placed on a vertical (or horizontal) line is

2. The triangle formed by a midpoint and two points of interception (marked blue) is a right triangle whose area is

3. The lens shaped area is the difference of a quarter circle and the blue right triangle

4. The shaded region's area is the difference of 4 circles and 8 lens shaped areas.