$3)$ Two I$-$beam designs $($shown below$)$ have been submitted for a project, and your engineering firm is tasked with evaluating the designs.

a$)$ Calculate area moment of inertia $\backslash (1$ x $\backslash )$ for design $\backslash ($ A $\backslash )$ and design $\backslash ($ B $\backslash ).$

b$)$ Calculate area moment of inertia ly for design $\backslash ($ A $\backslash )$ and design $\backslash ($ B $\backslash ).$

c$)$ What is the product of inertia Ixy $($for design $\backslash ($ A $\backslash )$ and design $\backslash ($ B $\backslash ))?$

d$)$ Calculate the polar moment of inertia $($Jo$)$ for design $\backslash ($ A $\backslash )$ and design $\backslash ($ B $\backslash ).$

e$)$ Your summer intern at the firm asks you "whats the difference between polar moment of inertia and area moment of inertia?" Explain what this is $($max $3$ sentences$).$

$30$ POINTS