Question

In the figure above, the hexagon with center O has six sides each of length 2 and six angles that each measure 120 degrees. What is the length of XY?

Answer 1

The lenght of xy line is equivalent to
then we take the top point and draw a line to our new line and use trigonometry


\[\cos 30° = \frac{ \frac{ a }{ 2 } }{2 }\]
now, cos30°=\[ \frac{ \sqrt{3} }{ 2 }\]
Finally \[a=2\sqrt{3}\]
and a=length of xy