17 is not allowed, just say it briefly.

Using the area of equilateral triangle ABC, the side length AB of triangle ABC is found to be 2, and similar triangles knows that triangle ADE is equilateral triangle. So AE= 1. The height of AE passing through point F is FG, and G is vertical foot. Let EG=M, then AG=FG= root number 3 times m. So? M+ root number 3 times M= 1M= (root number 3- 1)/2? So the area of triangle AEF = (root number 3 of 3)/4.

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