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 $\sin^{-1} 1=\frac{\pi }{2}$?

Is it at all possible to find the exact area of the circle without using $\pi$?