this Question is different from the other because it has angles.
We can use symmetry to solve this
The area of the 60 degree sector on the right is given by pi *12^2 * 1/6 = 144/6 pi =
24 pi units^2
The area of the triangle on the right = (1/2)(12^2)sqrt (3)/ 2 = 36sqrt3 units^2
So...half of the shaded area = the differences in these areas
So....the whole shaded area = twice this =
2 [ 24 pi - 36sqrt 3 ] = [48pi - 72sqrt3 units^2] ≈ 26.09 units^2