What is the area of a shaded segment with an area of 12 and an arch angle of 60

Let A = the area of the whole circle

Let S = the area of the shaded portion

The shaded area is a portion of the circle that is determined by the ratio of the shaded sector to the whole circle of 360 degrees, or

S = (60/360) * A = (1 / 6) * 12 = 2;