The area of the sector which is the white triangle adding the shaded region is 68.9/360*π*9.28^2=51.78005(rounding to 5th digit after decimal point for accuracy before we do final round for answer)
The area of the white triangle in the sector has area 1/2*9.28^2*sin(68.9)= 40.17223(rounding to 5 digits again for some accuracy.
Now we take out the white triangle from the sector.
51.78005-40.17223=11.60782
rounding to the nearest tenth we get 11.6 cm^2
Problem done!
Hope this helped and if you have any questions about my explanation just ask in the comment and I will answer.