Question

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

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

Answer 1

Answer: (D)

$6\sqrt{5}$

Given that the center of a regular hexagon is at origin and one of the vertices on axgand dig, $(1+2i)$

A regular hexagon is made up of 6 equilateral triangles. Thus the distance from the center to any vertex is equal to the length of an external side.

The center is loaded at $\left(0.0\right)$ and vertex at $(1,2).$ The radial distance from the origin to the vertex can be determined from the Pythagorean theorem :

$\Rightarrow r=\sqrt{1^2+2^2}=\sqrt{5}$

A regular hexagon has 6 equal sides. In this care, each sides length is $\sqrt{5}.$ The p[erimeter is $=6\sqrt{5}.$