jmc

Since the square has area 81 square units, it must have side length $\sqrt{81}=9$ units (all number lengths will be in units henceforth). The boundary consists of four straight segments of length $9/3=3$ and four quarter-circle arc segments. Notice how the four quarter-circle arc segments comprise a full circle of radius $3$; thus their total length is equal to that of the circumference of a circle of radius $3$, which is $6\pi$. The total length of the four straight segments is simply $3\cdot 4=12$. Hence the total length of both type of segments is $6\pi +12$, which is approximately 30.84956. To the nearest tenth, this value is $\boxed{30.8}$.