Problem $3.$ Consider the following composite shape. Note that the shaded is not part of the area.

The dimensions are in $mm.$

a$)$ Find the area of the shape.

b$)$ Find the location of the centroid.

c$)$ Find the moment of inertia about $x-$axis.

d$)$ Find the moment of inertia about $y-$axis.

e$)$ Find the moment of inertia about the axis passing through $x_c.$

f$)$ Find the moment of inertia about the axis passing through $y_c.$

g$)$ Find the moment of inertia about the point $C.$

Note: You can use the table given on the first page of the textbook: Geometric Properties of

Area Elements.

Hint: The shape is a composite section. The solution will utilize both Parallel Axis Theorem and

Perpendicular Axis Theorem.