The origin of $\pi$

The origin of $\pi$

How was $\pi$ originally found? Was it originally found using the ratio of
the circumference to diameter of a circle of was it found using
trigonometric functions? I am trying to find a way to find the area of the
circle without using $\pi$ at all but it seems impossible, or is it? If i
integrate the circle I get: $$4\int_{0}^{1}\sqrt{1-x^{2}}dx=4\left [
\frac{\sin^{-1} x}{2}+\frac{x\sqrt{1-x^{2}}}{2} \right ]_{0}^{1}=\pi $$
But why does $\sin^{-1} x=\frac{\pi }{2}$?
Is it at all possible to find the exact area of the circle without using
$\pi$?