The area of a circle is pi times the square of the radius. Pi has no relationship with the area of a polygon.
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area = pi*r2 where pi is the irrational number approximated by 3.14159
The area of a circle is defined by the equation A = πr^2 where π = pi (3.14...) A = Area r^2 = radius squared So, the radius of a circle squared multiplied by pi equals the area.
Pi and the radius can be used to find the area (PiR^2) or the circumference (2RPi) of a circle, where R is the radius.
pi (3.1416, etc) (or 22/7) is the fundemental constant (given or a priori) in the relationship between the area of a circle and its radius or diameter). i.e. area of a circle =Pi X R squared. Likewise the circumference is Pi X D where D is the diameter of the circle.
Pi is defined as the circumference of a circle divided by its diameter. This relationship carries a value of approximately 3.14159 as a constant. Additionally, Pi is defined also by a circle's area divided by its radius squared.