An equilateral triangle with side of 2 square root 3 is inscribed in a circle. what is the area of one of the sectors formed by the radii to the vertices of the triangle? 1.33 sq. in. 2 sq. in. 2.09 sq. in.

Refer to the figure.

We are looking for the area of the sector of a circle as shown in the figure shaded with green color. 

The area of a sector of a circle can be calculated using the formula 
     where r=radius, and θ=central angle (in radians)

The central angle of the given sector is just one-third of a full circle (2π). That is 
     

Now, to solve for the radius of the circle, we can use the formula
     
          where R is the radius of the circumscribed circle; a,b, and c are the sides of the triangle; and A is the area of the triangle.

The area of the equilateral triangle can be solved using the formula . That is 
     

Now, we substitute this area in the formula to solve for the radius of the circle. 
     

Finally, we can solve for the area of the sector by substituting the values of the angle θ, and the radius.
     

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