Question

Find the perimeter and area of the polygon with the given vertices. Round your answers to the nearest tenth, if necessary. E(6,2), F(6, 5), G( - 1, 5)​

Answer 1

$~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ E(\stackrel{x_1}{6}~,~\stackrel{y_1}{2})\qquad F(\stackrel{x_2}{6}~,~\stackrel{y_2}{5}) ~\hfill EF=\sqrt{(~~ 6- 6~~)^2 + (~~ 5- 2~~)^2} \\\\\\ ~\hfill EF=\sqrt{( 0)^2 + ( 3)^2}\implies EF = 3 \\\\\\ F(\stackrel{x_1}{6}~,~\stackrel{y_1}{5})\qquad G(\stackrel{x_2}{-1}~,~\stackrel{y_2}{5}) ~\hfill FG=\sqrt{(~~ -1- 6~~)^2 + (~~ 5- 5~~)^2}$

$~\hfill FG=\sqrt{( -7)^2 + ( 0)^2}\implies FG=7 \\\\\\ G(\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\qquad E(\stackrel{x_2}{6}~,~\stackrel{y_2}{2}) ~\hfill GE=\sqrt{(~~ 6- (-1)~~)^2 + (~~ 2- 5~~)^2} \\\\\\ ~\hfill GE=\sqrt{( 7)^2 + (-3)^2}\implies GE=\sqrt{58} \\\\[-0.35em] ~\dotfill\\\\ 3~~ + ~~7~~ + ~~\sqrt{58} ~~ \approx ~~ \text{\LARGE 17.6}$