If the circumference of a circle is 22 cm then the area of a quadrant of the circle is?

c := circumference of a circle = 2πr = 22cm
The radius r is then

r = c / (2π).

a := area = πr^2

A quadrant of the circle has the area

a / 4 = πr^2 / 4.

Now, let's put it together

r = 22cm / (2π) = (11 / π)cm.

a = π (11 / π)^2 cm^2 = 121π / (π^2) cm^2 = (121 / π) cm^2.

The quadrant is then:

121 / (4π) cm^2 = (30.25 / π) cm^2 ≈ 9.63 cm^2.