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(D) In a regular hexagon,the distance from the center to any vertex is equal to the side length of the hexagon.Let the center be $O(0,0)$ and one vert

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$6\sqrt{5}$

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(D) In a regular hexagon,the distance from the center to any vertex is equal to the side length of the hexagon.Let the center be $O(0,0)$ and one vertex be $z = 1 + 2i$.The distance from the origin to the vertex $z$ is the modulus $|z|$.$|z| = \sqrt{1^2 + 2^2} = \sqrt{1 + 4} = \sqrt{5}$.Since the hexagon is regular,the distance from the center to each vertex is the same,and the side length $s$ of the regular hexagon is equal to the distance from the center to any vertex.Therefore,the side length $s = \sqrt{5}$.The perimeter of a regular hexagon with side length $s$ is $6s$.Perimeter $= 6 	imes \sqrt{5} = 6\sqrt{5}$.

If the center of a regular hexagon is at the origin and one of the vertices on the Argand diagram is $1 + 2i$,then its perimeter is

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