What is the area of a circle with circumference 6pi?

Area = Pi x Radius^2

Diameter = Circumference / Pi

                  = 6Pi / Pi

                  = 6

Radius = Diameter / 2

              = 6 / 2

              = 3

Area = Pi x 3^2

         = 9Pi  square units.

The equation between a circle's radius and its circumference is as followed:

$Circumference=2πr$, with r being the radius.

Plug $6π$ into the equation:

$2πr=6π$

$2r=6$

$r=3$

We obtained the radius of your circle, now use the equation between a circle's radius to its area:

$Area=πr^2$

Plug $r=3$ into the equation

$Area=π*3^2$

$=9π$

Q.E.D.