I have the image below, where you cannot find real shape using Monte Carlo.
Same rasio but different shapes. The 1/2 rasio could have different shapes or angle, like triangle or half square or any shapes as the image above. But Monte carlo used to find rasio and just make sure that the rasio approximating 1/2.
the real rasio 1/2
after simulation 0.976767999 / 2
My question is, is it possible to find real shape using Monte Carlo? Since I have second day in Monte Carlo, I don't know the possibility.
I imagine you are performing this simulation by defining the region in the $xy$ plane and randomly generating points in the square / rectangle and you are approximating the area by finding the ratio of the number of points that fall in the region of interest to the total number of points.
There is no reason to say that a given run of the simulation isn't allowed to result in the exact area of the shaded region, but it isn't necessary. Of course this would require an even number of generated points; you can't end up with a ratio of $1/2$ with an odd number of points.
As you include more and more points, you are naturally going to result in answers that approach the exact area, since with a large number of points you should have points that span across much of the whole box, and the ratio will be close to exact. Could you by chance end up with the exact answer? Sure, but it is unlikely, nor is it the goal of Monte Carlo Simulation. The goal is to provide approximate answers to problems that might otherwise be impossible to solve through direct methods. However, it can also be used in your situation: a direct solution is easily seen but Monte Carlo Simulation can still be used so that you can see the process of how it works (and you can check your code to see if it is running properly)