$12.$ For the framing plan below, assume the structural slab weighs $55$ psf $,$ the steel framing weighs $10$ psf $,$ and there is a $15$ psf allowance for additional collateral $($MEP or miscellaneous$)$ dead loads. Live loads for each area and the slab span direction are as shown in sketch. Assume that the columns support $1$ floor.

a$)$ Determine the governing LRFD area loads applied to the Blue and Green Areas for unreduced live loads. $(1$ point$)$

b$)$ Determine tributary areas for Beams A and B$,$ Girders C and D$,$ and Columns E and $\backslash ($ F $\backslash ).(3$ points$)$