A composite shape is constructed from the same material all throughout using three rectangular sections $($A$,$ B$,$ and C$)$ and is placed on a flat plane. The composite shape dimensions is as follows:

Section A: A vertical rectangle with a height of $8$ ft and a width of $2$ ft $.$

Section B: A horizontal rectangle with a height of $2$ ft and a width of $8$ ft $,$ connected to the top of Section A$,$ centered horizontally.

Section C: A horizontal rectangle with a height of $1$ ft and a width of $10$ ft $,$ connected to the bottom of Section A$,$ centered horizontally.

A$)$ Find the centroid $($center of gravity$)$ of the entire composite shape.

B$)$ Calculate the moment of inertia of the composite shape about its centroidal axis.

${10}^{\text{'}}$