We know the equation for the circumference of a circle is: [tex] C=\pi d [/tex]
So when we plug in the given circumference of the circle, [tex] 2\pi [/tex], we get:
[tex] 2\pi =\pi d [/tex]
And solving for d, the [tex] \pi [/tex] cancels out. So we get:
[tex] d=2 [/tex]
We know that the area of a circle is found using the equation: [tex] A=\pi r^{2} [/tex], and that r is equal to half of d.
Therefore, we know that since the diameter of the circle is 2, the radius must be equal to 1.
So when we plug in the radius (1) for the area, we get:
[tex] A=\pi (1)^{2} [/tex]
[tex] A=\pi [/tex]
And now we know that the area of the circle is equal to [tex] \pi [/tex].
