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A PUZZLE IN INSTALLMENTS - 1

Quarantine is here, so extra time for solving puzzles. I have a proposal for you, which includes a daily problem regarding this figure and some related ones, constructed from points in a dodecagon, with a big reveal at the end. Are you game?
This is today's puzzle:

We have a circle with r=1, and 12 points for making a dodecagon. We join 7 of the vertices as shown.

What is the area of the resulting 14-sided polygon?
Same problem as yesterday: finding the area of polygons constructed from vertices of a dodecagon in a circle of r=1. Today we have 3 shapes, 1 symmetrical and 2 not.

They are related in a surprising way.
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