(Solved): 2. The Turkey - Centroid and Area Moment of Inertia (20 pts) "[the turkey is] a much more respectab ...

2. The Turkey - Centroid and Area Moment of Inertia (20 pts) "[the turkey is] a much more respectable Bird, and withal a true original Native of America...He is besides, though a little vain \& silly, a Bird of Courage." - Benjamin Franklin, comparing the turkey to the bald eagle After sitting down for dinner, you take a moment to examine the turkey and wonder if you could improve upon conventional engineering shapes by designing one inspired by the Bird of Courage. You take out your green engineering paper and sketch a bold new shape: A. Locate the centroid $(\stackrel{?}{x},\stackrel{?}{y})$ of the area. The white area for the "eye" of the turkey is a cutout and does not contribute to the cross-section. Note the $x$-axis and $y$-axis provided which give the origin of the area. Consult Appendix B as needed for centroid locations of simple shapes. Using a table is recommended: B. Determine the area moment of inertia of the cross-section with respect to the $X^{?}$ axis (shown in blue) that passes through the centroid of the area. You will determine the location of this axis in part $A$.