Help me with this!

ssolaming

New member
Joined
Mar 16, 2019
Messages
8
11501
I can tell that they have the same height, but what should i do next?
 

MarkFL

Super Moderator
Staff member
Joined
Nov 24, 2012
Messages
1,290
I would observe that, if we call \(r\) the radius of the circle in which the regular hexagon can be inscribed, then:

\(\displaystyle \overline{HI}=\frac{1}{2}r\)

And:

\(\displaystyle 2\overline{FI}+\overline{HI}=2r\)

See what you can do with that...:)
 

MarkFL

Super Moderator
Staff member
Joined
Nov 24, 2012
Messages
1,290
To add a bit of clarity to my previous post, consider the following diagram of a regular hexagon inscribed within a circle of radius \(r\), and decomposed into 6 equilateral triangles having side lengths \(r\):

fmh_0024.png

Now, in your diagram, we can see that \(\triangle GHI\) and \(\triangle GDE\) are similar, with the latter having twice the altitude of the former. And so the base of the latter, which is \(r\) will be twice the base of the former.

The rest of what I previously posted now follows. :)
 
Top