Find the area of the shaded region in the figure. (round your answer to one decimal place.) α = π/3, b = 12

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