Answer
The coordinates of the center of mass are $(5.0~cm, 6.7~cm)$
Work Step by Step
We can find coordinates of the center of mass for each of the three sides:
We can find the center of mass of the side on the left:
$x = 0$
$y = \frac{10.0~cm}{2} = 5.0~cm$
We can find the center of mass of the side on the right:
$x = 10.0~cm$
$y = \frac{10.0~cm}{2} = 5.0~cm$
We can find the center of mass of the section at the top:
$x = \frac{10.0~cm}{2} = 5.0~cm$
$y = 10.0~cm$
Let $M$ be the mass of each side. We can find the coordinates for the center of mass:
$x_{com} = \frac{M(0)+M(10.0~cm)+M(5.0~cm)}{3m} = 5.0~cm$
$y_{com} = \frac{M(5.0~cm)+M(5.0~cm)+M(10.0~cm)}{3m} = 6.7~cm$
The coordinates of the center of mass are $(5.0~cm, 6.7~cm)$.
