Hi everyone Just wondering if there are any mathematicians who can help me, I have a 9ft square area in the garden which I want to build an hexagonal pergola, is there anyone who can work out the lengths of each of the six sides? Thanks.

4'6" Draw a 9 foot dia. circle in the 9 x 9 foot square and divide into 6 segments of 60 degrees, add the 6 sides of the hexagon and you will see you have 6 isosceles triangles where all the sides are equal to the radius of the 9 foot dia circle.

The method of drawing a hexagon in school geometry lessons was to draw a circle using a compass, then use the compass around the perimeter of the circle to mark the hexagon's corners, quickly proving the radius of the circle was equal to the sides of the hexagon.

So work tomorrow, 6 x 4ft 6" cardboard cutouts 12" wide 60° angles bring home tape together set out and mark out posts, jobs a guddan.

As a general rule of thumb a regular hexagon will have sides 50% the length of the sides of a regular square - but you will need to have two opposite sides of the hexagon centred on the two opposite sides of the square. If you have all the sides at an angle to the sides of the square the answer will be different. Using bamboo canes, if you have some, will be the easiest way to show the right answer.

Or drive a peg into the ground at the centre, then tie a loop on a piece of string, place the loop over the peg, and cut the string to 4'6" long. Mark position of 1st post at end of string, rotate string around peg until the end is 4'6" from the 1st peg and mark position. Repeat until all 6 post positions have been marked.

Drawings of nuts and bolts was a favourite. Still got my 50+ years old drawing stuff, was using Autocad before I retired but now can't remember anything about it.