Question 17719
<font color=blue>
<pre>
   F ____E
    /\  /\
  A/__\/__\D
   \  /\  /
    \/__\/
    B    C
</pre>
Length AD=36 inches
Let the point of intersection of all the lines in the centre be O
</font>
<P>
Now,AO=OD=1/2 of AD
Then AO=(1/2)36=18 inches
Similarly,AO=BO=CO=DO=EO=FO
<P>
For a polygon with 'n' sides,the exterior angle is given by the formula:
{{{Ext=360/n}}}
For a hexagon,exterior angle=360/6=60 degrees
Therefore the interior angle is given by:
{{{Int=180-Ext}}}
Hence for a hexagon,interior angle is 180-60=120 degrees.
<P>
Therefore the angles for the hexagon is <font color=blue>120 degrees</font>
<P>
Hence angle ABC=BCD=CDE and so on for all the angles for the hexagon.
Then angle ABO=angle OBC=half of angle ABC
So angle ABO=(1/2)120=60 degrees
<P>
Now look at triangle AOB
<pre><font color=blue>
    O
    /\
   /  \
  A----B</font>
</pre>
Here,AO is equal to BO (proved earlier)
and angle ABO is 60 degrees.
Angle OAB is also 60 degrees (proved above)
<P>
Now the angle at the center O is 360 degrees,divided into 6 parts.
Hence each part is 60 degrees.
This means angle AOB=60 degrees
<P>
Then in triangle AOB,all three angles are 60 degrees.
It is an equilateral triangle with all equal angles,hence all its sides are also equal.
We know sides OA=OB.
Then side AB will also be equal to AO and OB
Therefore AB=18 inches.
This is the <font color=blue>length of the side of the hexagon=18 inches</font>
<P>
Angle=120 degrees,Side=18 inches
<P>
Hope this helps,
Prabhat