Minimum bedroom size - 7 foot in any horizontal direction
Whether you can make your space work or not, remember code requirements for a second exit besides the door- like an egress window, to get out in case of fire, etc. The Minimum escape area is 5'7" sq. ft.; with the  min. opening height is 24" high, and the width is 20". Also the sill has to be a maximum of 44" off the floor.
As far as the weird shape of the room, maybe you can go for a variance.