$2.$A surveyor sets up a transit at $P$ which is located in the middle portion of a four$-$sided tract of land and reads directions and measures distances, as given in the table below, to the corners. Find the area of the tract in square meters.

$\backslash$table$[[$Line$,$Bearing,Distance$],[$PA$,N41{30}^{\text{'}}W,410\mathrm{.}52],[$PB$,N38{10}^{\text{'}}E,532\mathrm{.}18],[$PC$,S70{20}^{\text{'}}E,450\mathrm{.}75],[$PD$,S60{15}^{\text{'}}W,590\mathrm{.}08]]$