
How to construct a hexagon, a regular 6sided polygon, given one side?

1. 
 Start with the construction of an equilateral triangle with the same given side.


2. 
 Draw a circle with the center at the top of the triangle, and a radius equal to one side of triangle 1.


3. 
 Draw an arc with its center at the left angular point of triangle 1, and a radius equal to one side. It must intersect circle 2 twice (once in the angular point on the right).


4. 
 Draw the connecting line between the center of arc 3 and the second intersection of it with circle 2.


5. 
 Draw the connecting line between the last mentioned intersection (4) and the top of triangle 1, and extend it until it intersects circle 2 a second time.


6. 
 Draw the connecting line between the right angular point of triangle 1 and the last mentioned intersection (5).


7. 
 Extend the left side of triangle 1 until it intersects circle 2 a second time.


8. 
 Repeat this for the right side of triangle 1.


9. 
 Draw the connecting line between consecutive intersections of circle 2, first between intersections 5 and 7.


10. 
 Next between intersections 7 and 8.


11. 
 Finally between intersections 8 and 3.


12. 
 Lines 4, 6, 9, 10 and 11, together with the baseline of triangle 1, form the hexagon to be constructed.

