#1**+1 **

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

CPhill
Oct 14, 2018