Opinions on the definition of roof perimeter for this flat roof
Disreguard the mansard sections of that flat roof and just consider the perimeter as flat (attached).
Its still ‘Other’. The flat is greater than 10% & structurally attached. Even though its surrounded by hip geometry, the flat is still considered a non hip feature.
Sorta reminds me of a mansard. It’s a non-hip or other even though as Jay has pointed out it’s surrounded by a hip geometry.
Bert
Just thought I would throw this out for discussion. I agree with Jay but thought it might be helpful for others 
Yes Fred. Thanks it’s a very good post and thought provoking for sure.
Bert
Yes, great post. It is likely one of the biggest points of confusion for some. I have had to explain it repeatedly to everyone involved whenever we run into this kind of roof feature.
You would measure the perimeter of the flat as your “other” and the perimeter of the roof as total perimeter.
I would only count 3 legs of the flat roof perimeter as “other”…omitting the length that is common to the hip roof. But then again, I don’t teach wind mit classes.
You are correct. 
Total 293’
Other 53’ ( 3 legs of flat)
greater than 10% Roof Shape " Other"
Thank guys Hope this helps all that run into something like this 
Just to stir it up;
Does any inspector believe that this is not a hip roof, setting aside the 1802 def.
The angles/pitch of the roof is not taken into consideration when cal the total of roofing.
Check to see if your home mit liability ins is adequate.
In my opinion, The home owners are fighting back and the crap that is being instructed in the mit classes has been tainted by the ins industry. The A/E’s and bldg officials will be called as expert witnesses in court.
Do your research, work hard and be honest.
Maybe I’ll pose a couple of these questions at the class next week!