$\"\"$

Centroids of the region is $\"\"$ and $\"\"$ .

Area is $\"\"$ .

Center of mass of lamina if the square portion of lamina is twice the density of lamina.

Therefore Mass is $\"\"$ .

The center of mass $\"\"$ is $\"\"$ and $\"\"$ .

Where $\"\"$ .

Here $\"\"$ is the total mass of the system.

$\"\"$

$\"\"$ is $\"\"$ as the $\"\"$ coordinates are $\"\"$ .

Therefore the center of mass is $\"\"$ is $\"\"$ .

$\"\"$

The center of mass is $\"\"$ is $\"\"$ .