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Star Gazing

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.

In or Out?

Age 14 to 16 Short Challenge Level:

The shaded region shown in the diagram is bounded by four arcs, each of the same radius as that of the surrounding circle.

What fraction of the surrounding circle 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.
You can find more short problems, arranged by curriculum topic, in our short problems collection.