$(8$ points $)$

Consider a symmetric cross $($over the x and y axis$)$ inscribed in a circle of radius r$.($Show all work$)$

$($a$)$ Write the area A$($x$)$ of the cross as a function of x and find the value of x that maximizes the area.

$($b$)$ Write the area A$($theta$)$ as a function of theta and find the value of theta that maximizes the area.

$($c$)$ Show that the critical numbers of parts $($a$)$ and $($b$)$ yield the same maximum area. What is that area?