2018 AMC 12B Problem #16

Geometry Level 3

The solutions to the equation ( z + 6 ) 8 = 81 (z+6)^8 = 81 are connected in the complex plane to form a convex regular polygon, three of whose vertices are labeled A , B , A, B, and C . C. What is the least possible area of △ A B C \triangle ABC ?

This problem is part of the 2018 AMC 12B .
2 3 − 3 2 2 \sqrt{3} - 3 \sqrt{2} 3 2 2 − 3 2 \dfrac{3}{2} \sqrt{2} - \dfrac{3}{2} 1 2 2 \dfrac{1}{2} \sqrt{2} 3 − 1 \sqrt{3} - 1 1 6 6 \dfrac{1}{6} \sqrt{6}

Steven Yuan by Steven Yuan , 20, USA

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