The radius at the middle part of the trangle growing bigger to match the side line length. So at the sides, side line > radius.
When entering the circle area, why suddenly both radius and side line become EQUAL ??? 👏👏👏
(The above illustration was taken randomly from Google).
There has been a corruption of calculation, when longer sized side lines (CB & CA) are treated the same size as the radius (CD).
In fact CB > CD as much as CA > CD.
So for circular area you should substract your existing assumption about its calculation.
Circular Area ain’t equal 1/2r.C.
The true Circular Area equals 1/2r.C – X.
X = area substraction due to the adjustment or shortening of side lines to be as far as the radius length.
For area, pi is right.
But the assumption of C should be rethought.
C is bigger than what is assumed so far.
If straight line of C becomes circular, Archimedes method will find pi as constant of area, but remember, this pi’s area is the result of area substraction as the inevitable consequence after the side line radiuses is shortened to be as far as the actual radius.
Pi’s area is okay – series confirms it – but you should add the size of your assumption about C.