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How Shady?

Age 11 to 14 Short Challenge Level:

The diagram below shows an equilateral triangle with some triangles shaded inside it.

Each shaded triangle is equilateral and touches the sides of the largest triangle and of the shaded triangles next to it.

What fraction of the whole triangle is shaded?






This problem is taken from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.