Before revision:  In this paper, we present a new sufficient condition for packing circles into any right or obtuse triangle using only the circles' combined area: It is possible to pack any circle instance whose combined area does not exceed the triangle's incircle .
After revision:  In this paper, we present a new sufficient condition for packing circles into any right or obtuse triangle using only the circles' combined area: It is possible to pack any set of circles with a combined area of up to approximately 53.90\% of the square's area. And when the container is a right or obtuse triangle, any set of circles whose combined area does not exceed the triangle's incircle .