Cutting shapes

I was asked to do some demonstration at this month’s IPS branch meeting which was on yesterday now. I pondered idea what to do for a while and decided to do about Y-seam.
And that involves cutting not square shapes like diamonds, trapezium and hexagon. I got this equilateral triangle ruler a while back from Creative Grid and wondering what else I can do other than cutting triangle shapes (I have two more in my shop if you are interested).

 
The first pattern to tackle was this. I can’t find the name of this pattern and if you know please let me know!
The single block is made of three trapeziums.

Those angles are 60 and 120 degree and I should be able to use that ruler but I couldn’t figure out the length of trapezium. But I accidentally found it!
I cut the fabric 2.5″ wide which ends up 2″ when sewn. Then I put the 2″ mark of the ruler to the edge of fabric and cut the both ends.

It fitted perfectly! I tried with 3″ and it was perfect too. I can’t figure out math side of this but it works on any size which I have tried and proven on the drawing program.

So to cut the trapezium shape to make triangle pattern, place the marking of the ruler of desired finished width of trapezium on the edge of strip which cut as required and cut the shape.
 
Addition to that I was explaining how to cut the hexagon shape with this triangle ruler in a slightly slow way at the meeting and on the way home I realised I can apply the theory above to the hexagon too.
Cut the fabric in strip with 1/2″ seam allowance and fold in half. This one is again 2.5″ wide.

Find the half the width of the finished strip. In this case 1″ because finished strip is 2″. Place the mark of ruler of that half the width on the raw edge of fabric, not the fold. In this case 1″ marking is on the raw edge. And cut!

And you will have a perfect hexagon!