$(30pts)$ The Statue of Liberty is an immense structure whose external copper "shell" is supported

internally by an intricate steel truss system as shown in the example image. In two dimensions, her arm

can be considered approximately as a parallelogram, her torch a square, and the flame on the torch

approximately circular as shown. If the copper arm, torch, and flame have an approximate density of

$8,850k\frac{g}{m^{{?}^{{?}^{?}}}}2$ and is pinned to the truss structure at points $E$ and $F,$ determine the following:

a$)$ The net centroid of the arm, torch, and flame system relative to point F$.$ Note the centroid of a

parallelogram is the center point of its diagonal $\{\frac{x1+x2}{2},\frac{y1+y2}{2}\}$

b$)$ The reaction forces at the base of the support truss $($Points A and I$)$

c$)$ If the maximum load any $1$ member can withstand is $2800kN,$ determine which members will fail.

Write down ALL members that would fail.