The problem may seem very hard but it isn't really is.
The idea is that we can break any polygon into triangles, these triangles will be of the form
We can then find square such that
And then we can find a square such that
And if we are able two add at least 2 square then we can find the sum.
So we are first going to break the problem in two parts :
Squaring A Triangle
Adding Two Squares
So we are done!
denotes the area of planar figure
If anybody need justification of any of the construction he or she may ask. (Although they are much easier to be justified)
The number of steps for squaring an polygon shall be increasing linearly if we used these steps, if anybody can do this in less amount of steps then please comment.
If anybody can prepare an animation of this either in Desmos or in .gif format etc, please share it here.