Geometry
# General Polygons

The following figure shows an irregular hexagon with six circles of radius 1 where the hexagon's vertices are circles' centers.

Find sum of the areas of the black regions.

**True or False?**

\(\quad\) **Statement I**: If all sides of a polygon are equal, then all angles of the polygon are equal.

\(\quad\) **Statement II**: If all angles of a polygon are equal, then all sides of the polygon are equal.

I am a peculiar quadrilateral. If you put 3 copies of me together, then I can form an equilateral triangle. Similarly, if you put 3 copies of an equilateral triangle together, then they can form me!

What quadrilateral am I?

**enneagon** (9-sided polygon)?

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