Question

From a square sheet of uniforms density a portion is removed then find its center of mass of side a square

Answer 1

Lets find out the com of the triangle first.
Let the density be 
The center of the squre is taken as the origin
The x coordinate of the CoM is

Now using symmetry 
Similarly, the coordinates of the other three triangles are (-a/3,0), (0,a/3),(0,-a/3)
So the CoM of the remaining square is