$4\mathrm{.}8.$ A uniformly illuminated rectangular aperture situated in the x$-$y plane is $3-$meter$-$high $($along x$)$ and $1$ meter wide $($along y$).$ If f$=10$GHz$,$ determine, $($a$)$ the beam width of the radiation pattern in the elevation plane $($x$-$z plane$)$ and the azimuth plane $($y$-$z plane$),$ and $($b$)$ the antenna directivity D in decibels