The figure below is a regular hexagon dissected into a triangle, a rhombus, and a trapezoid.

**If the area of the blue triangle is $3,$ what is the area of the red trapezoid?**

**Try this riddle:**

I am a peculiar quadrilateral. If you put 3 copies of me together, 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?**

Definitions:

- parallelogram
- trapezoid
- rhombus

A **dissection** of a polygon is a pattern for cutting one polygon up into many polygonal pieces. The hexagon dissection below uses a combination of all of the pieces in the six-pointed star *and* all of the pieces in the dissection of the triangle with a small hole in the center.

If the star has an area of 20, what is the area of the hexagon?

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