In the given question, we have an equilateral triangle inscribed in a circle of radius 1 unit. We need to find the area of the shaded region.

To solve this problem, we can divide the shaded region into three equal sectors of the circle, each corresponding to one side of the equilateral triangle. Since the circle has a radius of 1 unit, each sector will have an angle of 120 degrees.

The formula to find the area of a sector is ([REPLACEMENT]/360) * π * r^2, where [REPLACEMENT] is the angle of the sector, and r is the radius of the circle. Plugging in the values, we get (120/360) * π * 1^2 = (1/3) * π.

Since there are three sectors, the total area of the shaded region is 3 * (1/3) * π = π.

So, the correct answer is option 1, which represents the area of the shaded region as π.