Question

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

• A. $2\sqrt{5}$
• B. $6\sqrt{2}$
• C. $4\sqrt{5}$
• D. $6\sqrt{5}$

Answer 1

The correct option is D $6\sqrt{5}$

Length of the sides of the regular hexagon will be equal to the distance of the vertex from the origin $=\sqrt{1^2+2^2}$
$=\sqrt{5}$
Hence perimeter will be
$=6\left(sidelength\right)$
$=6\left(\sqrt{5}\right)$