Finding the Center of Mass of a Triangle

For x_com, upon fixing sign errors, the fractions 1/2 and 1/3 are subtracted giving -1/6 a^2 and 1/6 b^2. So x_com = (b - a)/3. Note b-a makes sense since for larger b there is more mass in the positive x axis. For a=1.2, b=0.3, theoretical x_com = - 0.9/3 = - 0.3. So the Monte Carlo simulation result is off by 1%. Very Good!

What an amazing video!!! So fun to watch even though I didn't really understand the stuff you wrote on the paper haha

Geometric centre can be different from com of an object. That depends on mass distribution of object regardless of shape.