April 2015 - Hexagons Inside Hexagons

There is a large regular hexagon. There are two other regular hexagons that meet at the centre of the large hexagon. Now, two other hexagons are in the space between the other two and the sides of the large hexagon. This creates two small equilateral triangles. Finally, two small hexagons are drawn inside these triangles. The shaded area is 41 square units. What is the unshaded area of the large hexagon?

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