To calculate for the area of the shaded region, we can find for the area of the unshaded part and subtract it to the area of the whole circle. We do as follows:
Height of the triangle = cos(30) x 12 = 6√3
Area of the triangle = 0.5bh = 0.5(12)(6√3) = 36√3
Area of the circle = πr^2 = π(12^2) = 144π
Area of the unshaded region = π(12^2) (60/360) - 36√3 = 24π - 36√3
Area of shaded = 144π - 24π +36√3 - 36√3
Area of shaded = 120π
