This mansard extension has a flat roof.
ROOF EXTENSION B: MANSARD ROOF
This design would work under permitted development rules for the rear of a house, allowing most of the rear half of the loft space to be used as extra rooms. The size is limited, depending on the type of house (terraced, semi-detached, or detached). The materials should match the roof of your house.
The rear wall slopes away from the rear of the house.