Geometry

# General Polygons: Level 2 Challenges

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

Find the 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 is the maximum number of interior right angles than can be used to form an irregular enneagon (9-sided polygon)?

Andrew draws a certain polygon with five sides such that its interior angles are two times, three times, four times, and eight times the smallest interior angle respectively. What is the measure of smallest interior angle in degrees?

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