Question

How do you find the circumference when you ONLY know the area?

Answer 1

It's easy if you remember the formulas you learned for the area, diameter,
and circumference of a circle:

-- Area = (pi) (radius)²
-- Diameter = (2) (radius)
-- Circumference = (pi) (diameter)

You know the area. So let's use the first formula to find the circle's radius.

Area = (pi) (radius)²

Divide each side by (pi):      Area/pi  =  (radius)²

                                            Radius = √(area/pi)

Now use the second formula to find the circle's diameter:

Diameter = (2) (radius)

Diameter = 2 √(area/pi)

Now use the third formula to find the circle's circumference:

Circumference = (pi) (diameter)

Circumference = (pi) (2) √(area/pi)

With just a little tweak, that can be written slightly more simply:

Circumference = 2 √(pi x area)

See ?  Just the three circle formulas,and a lot of massaging.