The red area is the difference in the area of the sector less the area of the isosceles triangle with the radius as its equal sides
Area of sector = pi * r^2 * (68.9 / 360) = pi *(9.28)^2* (68.9 / 360) (1)
Area of triangle = (1/2) (r^2 ) sin (68.9°) = (1/2) (9.28)^2 sin (68.9°) (2)
So.....the red area = (1) - (2) =
[ pi *(9.28)^2* (68.9 / 360) ] - [ (1/2) (9.28)^2 sin (68.9°) ] =
51.78 - 40.17 ≈
11.6 cm^2