We can find the area of the segment by subtracting the area of the triangle (A_triangle) from the area of the sector (A_sector).
A_segment = A_sector - A_triangle
We then find the value of each variable. For the sector of the circle, we use the equation: A_sector = (angle/360)(pi*r^2)
Plugging in the values we will have
A_sector = (68.9/360)(pi*9.28^2) = 51.8
Now for the triangle, area is simply 1/2 * base * height. Since two sides of the triangle have the radius as the angle, and the angle between them given, we then use the formula A_triangle=1/2ab(sin C). Where in C is the given angle, and a and b are the corresponding sides.
A_triangle = (1/2)(9.28)(9.28)(sin 68.9)
A_triangle = 40.2
All that is left for us is to subtract the triangle area from the sector area.
A_segment = 51.8 - 40.2
A_segment = 11.6 square centimeters