Question $1[20$ points$]$

Given the coordinates $($in ft$)$ of the stations in the traverse on slide #$57$ in Lecture $6,$ find the area of

the polygon using the coordinates method.

Station North East

A $1,089\mathrm{.}981935\mathrm{.}049$

B $1,000\mathrm{.}0001,000\mathrm{.}000$

C $1,078\mathrm{.}7541,068\mathrm{.}139$

D $1,046\mathrm{.}6351,205\mathrm{.}498$

E $1,154\mathrm{.}3661,030\mathrm{.}252$