Two position vectors each start at the origin. The first has a magnitude of $45\mathrm{.}5$ cm$,$ and is at an angle of $15\mathrm{.}0$ as measured counterclockwise from the $+$x$-$axis. The second has a magnitude of $23\mathrm{.}0$ cm and an angle of $73\mathrm{.}0,$ also counterclockwise from the $+$x$-$axis.

$($a$)$

What is the area of the parallelogram $($in cm$2)$ that has the two vectors as two of its sides?

cm$2$

$($b$)$

What is the length of the longer diagonal of this parallelogram $($in cm$)?$

cm