Geomegebra

Algebra Level 1

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

2 5 2\sqrt { 5 } 4 5 4\sqrt { 5 } 6 5 6\sqrt{5} 5 5 5\sqrt { 5 }

View wiki
Gaurav Adusumilli by Gaurav Adusumilli , 23, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Arjen Vreugdenhil
Sep 18, 2015

A regular hexagon has the property that (distance between center and vertex) = (length of a side).

Distance between center and vertex = ∥ 1 + 2 i ∥ = 1 2 + 2 2 = 5 , \|1+2i\|=\sqrt{1^2+2^2}=\sqrt{5}, so that the perimeter is 6 5 . □ 6\sqrt{5}.\square

6 Helpful 2 Interesting 0 Brilliant 0 Confused
Rohan Gupta
Apr 29, 2015

A regular hexagon can be divided into 6 equilateral triangles. So distance from origin to the vertex is equal to the length of the side of hexagon. Let a a be the side of the hexagon. Therefore a = 1 + 4 = 5 a=\sqrt{1+4} \\ =\sqrt 5 Hence the perimeter is 6 5 . □ 6 \sqrt 5. \square

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...