The formula for circumference of a circle is [tex] d\pi [/tex], where [tex] d [/tex] is the diameter of the circle. Given this, we can find our diameter:
[tex] d\pi = 4\pi x [/tex]
[tex] d = 4x [/tex]
The formula for the area of a circle is [tex] \pi r^2 [/tex], where [tex] r [/tex] is the radius of the circle. Given this, we can find the area of our circle:
[tex] 4x = d = 2r [/tex]
[tex] r = 2x [/tex]
[tex] \pi(2x)^2 = \boxed{4\pi x^2} [/tex]
