Finding the area of a circle

In order to find the area of a circle we need to use the equation area equals pi r squared. We can either estimate the area of a circle by putting a numeric value to pi or use pi as an infinite value that will find the area of a circle. Either way we are not finding an exact numeric value to the area of a circle.. if the area of a circle is finite. There is an exact area within a circle. But we yet to have an equation that can give you an exact numeric value to the area of a circle.

Am I correct in my analysis?