Geometry

First, draw an equilateral triangle inside the shaded area. One side should be 6cm in length

There should also be two semi-circular shapes outside the triangle.

The area of the triangle - (using the Pythagoras theorem, we know that the height of the triangle is sqrt of 26)

3 6 sqrt(26)/2 = 3*sqrt(26)

The area of two semi-circular shapes - 6 * 6 * 3.14 * 60/360

18.84*2=37.78

37.78 - 3*sqrt(26) =22.482941

I recognized the two curves as the equations x=sqrt(36-y^2) and x=-sqrt(36-y^2)-6. Subtracting the two functions results in 2 sqrt(6-y) sqrt(6+y)-6. Integrating from 0 to 3×sqrt(3) - that is the y value the two funtions intersect - provides the result 12×pi-9×sqrt(3). Approximating the result gives 22.11. This isn't equal to any answers, but the closest answer is 22.48 which is correct.