Help quick

Nope, still not correct     Ooops....  back to the drawing board......

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! )}

The smaller area  is the  difference between the area of a sector  of 1/6 of the circle  less the area of a equilateral triangle with a side of 6.....this is given by

[(1/6) pi * 6^2   -  (1/2)6^2 * √3/2  ]    (1)

So....the   larger area  =

Area  of circle  - (1) 

So

pi*6^2  -   [(1/6) pi * 6^2   -  (1/2)6^2 * √3/2  ]  =

(5/6) pi * 6^2  + 9√3   =

[30pi + 9√3] units^2