Constructing an irregular roof

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Hi there,

We have a small boiler room extension at the back of our house, with a shed/lean-to style roof.

We are extending this to make a small study. Unfortunately due to the layout of the property we have a very small amount of room to extend, especially on one side due to a retaining wall that cannot move.

The result is that the room will not be rectangular - it will have one side 0.9m and one of 1.3 projecting from the house (distance across house wall is 1.8m.

We cannot just extend the roof out equally because the retaining wall would be in the way. So I am trying to work out how the roof joists would need to be designed - and it's seriously hurting my head (I am not good at thinking in 3D!)

Has anyone done a similar project? I have build both a gable/apex and a shed/lean-to roof before, but never on anything that wasn't square.
 

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