Definitely isn't Petworth and too far west to be Brookland. I've always considered that area to be Fort Totten.
The area is mostly working class to middle class and about 70-80% African American. You have two bus routes that serve that area which are the #H8 crosstown
http://www.wmata.com/bus/timetables/dc/h89.pdf and the #60
http://www.wmata.com/bus/timetables/dc/60-64.pdf. The H8 runs 7 days week and goes from Rhode Island ave station and through Brookland then across the red line tracks on Bryant street then goes through the area you've mentioned then crosses North Capitol street into Petworth and through Columbia Heights then finally Mt. Pleasant. It's a good bus line that'll pretty much take you where you need to go to. The 60 on the other hand only operates 5 days a week and the hours are limited, its more-so of a go to/from work and school type of bus line.