The measure of central angle abc is pi/2 radians.

what is the area of the shaded sector?

     It the measure of central angle ABC is π/2 radians ( 90° ) then the shaded sector represents 1/4 of the area of the circle.
     Area of the circle:
    A = r² π = 6² π = 36 π
    A ( ABC ) = 36π : 4 = 6 π
   
    6 π units².