Star in a Hexagon

Weekly Problem 20 - 2017
The diagram shows a design formed by drawing six lines in a regular hexagon. What fraction of the hexagon is shaded?
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Problem



Image
Star in a Hexagon


The diagram shows a design formed by drawing six lines in a regular hexagon. The lines divide each edge of the hexagon into three equal parts.

What fraction of the hexagon is shaded?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.