Our house was extended in 1932 and a small flat roof was used above a corner window. We never liked the style of this roof and it also had problems with water leakage so in 2012 we have decided to replace it with a small tiled hipped roof.
I've used a hipped roof to maintain visual compatibility with the rest of the house. As described on Wikipedia: "A hip roof, or hipped roof, is a type of roof where all sides slope downwards to the walls, usually with a fairly gentle slope. Thus it is a house with no gables or other vertical sides to the roof."
This web site provides a detailed photographic record of what was involved in building it along the lines of a previous web site of ours: www.myhouseextension.com.