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Gaudi's Design

Stage: 3 and 4 Short Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The diagram shows a ceramic design by the Catalan architect Antoni Gaudi. It is formed by drawing eight lines connecting points which divide the edges of the outer regular octagon into three equal parts, as shown.

What fraction of the octagon is shaded?

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

This problem is taken from the UKMT Mathematical Challenges.
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