Draw a line from the center to each of the endpoints of the chord
this forms a equilateral triangle the central angle is 60 degrees (pi/3 radians)
the area of this sector is 60/360 of the TOTAL area of the circle
pi r^2 x 60/360 = 6 pi
Now subtract the area of the equilateral triangle to get the area enclosed by the chord
area of equalateral triangle = r^2 (sqrt3) / 4 = 9 sqrt3
6pi - 9 sqrt3 = area of chord
Total area of cicle - area enclosed by chord = larger area
36 pi - ( 6pi - 9 sqrt3)
30 pi + 9 sqrt3 units2
(there has to be a better way! )