Problem $7$: Top flange is $6^{\text{'}\text{'}}$ wide and $1^{\text{'}\text{'}}$ thick.

Bottom flange is $2^{\text{'}\text{'}}$ wide and $1^{\text{'}\text{'}}$ thick.

Web is ${10}^{\text{'}\text{'}}$ tall and $1^{\text{'}\text{'}}$ thick.

Determine the centroid location for $x$ and $y.$

Determine the moment of inertia with respect to $x.$ Show all work.