You need 40 square feet of room for your coop(8x5, 6x7, or 10x4 area). You will need more space if your planning on increasing your flock in the future. Look at the different coop plans on this site and pick what you like. My dh built a 12x4x8 rectangular room in our garage for our 8 chicks. Good luck.
If you need a triangle coop and need 40 square feet of space, you will need to make one side of the coop 8ft and the other 10ft. The long side that will face out should then be about 12.8 ft. (If my math is correct)! That will give you 40 sq. ft.
The amount of space you need also depends on the breed. Jersey Giants need more room than Ameraucana which need more room than bantams. It also depends on whether they are in the coop all the time or simply to lay and sleep. A calc. that is often used for "large fowl" is 3 s.f. per layer indoors and 10 s.f. of outdoor run space. If you have roosters you'll need more.
Your math is correct. Seems that if you make a triangular coop and a 9x9 roof then you'll have a nice covered area for access if its raining and also a possible storage area for pine shavings, food... you could then just do a single sloped roof. You could then place the clean out doors at the front (12ft side) and then the nest boxes on one of the sides (9ft). At least those are my thoughts.