Problem $3$: $(4$ points$)$ For a triangle with a horizontal base and a

vertical height, determine the first moment of inertia about an

axis passing through its base. From this, calculate the location

of its centroid above its base.

Problem $4$: For a rectangle with a horizontal base and a vertical

height, determine:

a$)(3$ points$)$ The first moment of inertia about an axis passing

through its base. From this, calculate the location of its

centroid above its base.

b$)(3$ points$)$ The first moment of inertia about an axis passing

through its centroid.

c$)(4$ points$)$ The second moment of inertia about an axis

passing through its centroid