Question

Find the perimeter of the shape below:

Answer 1

Check the picture below.

`~\hfill \stackrel{\textit{\large distance between 2 points}}{d = √(( x_2- x_1)^2 + ( y_2- y_1)^2)}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ S(\stackrel{x_1}{-2}~,~\stackrel{y_1}{7})\qquad R(\stackrel{x_2}{-1}~,~\stackrel{y_2}{3}) ~\hfill SR=√((~~ -1- (-2)~~)^2 + (~~ 3- 7~~)^2) \\\\\\ ~\hfill SR=√(( 1 )^2 + ( -4)^2) \implies \boxed{SR=√( 17)}`

`R(\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad U(\stackrel{x_2}{-1}~,~\stackrel{y_2}{5}) ~\hfill RU=√((~~ -1- (-1)~~)^2 + (~~ 5- 3 ~~)^2) \\\\\\ ~\hfill RU=√(( 0)^2 + ( 2)^2) \implies RU=√( 4)\implies \boxed{RU=2} \\\\\\ U(\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\qquad T(\stackrel{x_2}{2}~,~\stackrel{y_2}{5}) ~\hfill UT=√((~~ 2- (-1)~~)^2 + (~~ 5- 5~~)^2) \\\\\\ ~\hfill UT=√(( 3)^2 + ( 0)^2) \implies UT=√( 9)\implies \boxed{UT=3}`

`T(\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad S(\stackrel{x_2}{-2}~,~\stackrel{y_2}{7}) ~\hfill TS=√((~~ -2- 2~~)^2 + (~~ 7- 5~~)^2) \\\\\\ ~\hfill TS=√(( -4)^2 + ( 2)^2) \implies \boxed{TS=√( 20)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Perimeter} }{√(17)+2+3+√(20) }~~ \approx ~~ \text{\LARGE 13.6}`