#### Answer

(a) The coordinates of the center of mass are (5.7 cm, 4.6 cm)
(b) $I = 0.0066~kg~m^2$

#### Work Step by Step

(a) Note that mass $A$ is located at the origin.
We can find the x-coordinate of the center of mass.
$x_{com} = \frac{(100~g)(0)+(200~g)(0)+(200~g)(10~cm)+(200~g)(10~cm)}{100~g+200~g+200~g+200~g}$
$x_{com} = 5.7~cm$
We can find the y-coordinate of the center of mass.
$y_{com} = \frac{(100~g)(0)+(200~g)(8~cm)+(200~g)(8~cm)+(200~g)(0)}{100~g+200~g+200~g+200~g}$
$x_{com} = 4.6~cm$
The coordinates of the center of mass are (5.7 cm, 4.6 cm)
(b) We can find the moment of inertia about an axis located at the origin. Note that mass $C$ is located a distance of 12.8 cm from the origin.
$I = \sum m_i~r_i^2$
$I = (0.10~kg)(0)^2+(0.20~kg)(0.08~m)^2 + (0.20~kg)(0.128~m)^2+ (0.20~kg)(0.10~m)^2$
$I = 0.0066~kg~m^2$