If the area of a circle is pi*R squared, shouldn't it be pi*C?

$$C=2\pi r = \pi r+ \pi r\\

A=\pi r^2 = \pi\times r\times r$$

$$\pi\times C=\pi \times 2\pi r = 2\pi^2r\ne A$$

Does that help?

No, because the radius and circumference aren't the same thing.