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The diagram has rotational symmetry of order four about $D$.


If angle $ABC$ is $15^{\circ}$ and the area of $ABEF$ is $24$cm$^2$, what is the length of $CD$?

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

 

 

This problem is taken from the UKMT Mathematical Challenges.