Question

The coordinates of the vertices of a polygon are (-2, -1), (-2, 3), (2, 3), (2, 0), and (1,-4).

What is the perimeter of the polygon to the nearest tenth of a unit?

Answer 1

Check the picture below.

so hmmm let's only find the lines in red and add them up all

`~\hfill \stackrel{\textit{\large distance between 2 points}}{d = √(( x_2- x_1)^2 + ( y_2- y_1)^2)}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{-2}~,~\stackrel{y_1}{-1})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-4}) ~\hfill d1=√((~~ 1- (-2)~~)^2 + (~~ -4- (-1)~~)^2) \\\\\\ ~\hfill d1=√(( 3)^2 + ( -3)^2) \implies d1=√( 18 )`

`(\stackrel{x_1}{1}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{0}) ~\hfill d2=√((~~ 2- 1~~)^2 + (~~ 0- (-4)~~)^2) \\\\\\ ~\hfill d2=√(( 1)^2 + ( 4)^2) \implies d2=√( 17 ) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Perimeter}}{4~~ + ~~4~~ + ~~3~~ + ~~√(18)~~ + ~~√(17)} ~~ \approx ~~ \text{\LARGE 19.4}`