Question

What is the perimeter of this quadrilateral?
(5,5)
(2, 4)
(4, 1)
(6, 1)

Answer 1

`~\hfill \stackrel{\textit{\large distance between 2 points}}{d = √(( x_2- x_1)^2 + ( y_2- y_1)^2)}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{5}~,~\stackrel{y_1}{5})\qquad B(\stackrel{x_2}{2}~,~\stackrel{y_2}{4}) ~\hfill AB=√([ 2- 5]^2 + [ 4- 5]^2) \\\\\\ AB=√((-3)^2+(-1)^2)\implies \boxed{AB=√(10)} \\\\[-0.35em] ~\dotfill\\\\ B(\stackrel{x_1}{2}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{4}~,~\stackrel{y_2}{1}) ~\hfill BC=√([ 4- 2]^2 + [ 1- 4]^2)`

`BC=√(2^2+(-3)^2)\implies \boxed{BC=√(13)} \\\\[-0.35em] ~\dotfill\\\\ C(\stackrel{x_1}{4}~,~\stackrel{y_1}{1})\qquad D(\stackrel{x_2}{6}~,~\stackrel{y_2}{1}) ~\hfill CD=√([ 6- 4]^2 + [ 1- 1]^2) \\\\\\ CD=√(2^2+0^2)\implies \boxed{CD=2} \\\\[-0.35em] ~\dotfill\\\\ D(\stackrel{x_1}{6}~,~\stackrel{y_1}{1})\qquad A(\stackrel{x_2}{5}~,~\stackrel{y_2}{5}) ~\hfill DA=√([ 5- 6]^2 + [ 5- 1]^2)`

`DA=√((-1)^2+4^2)\implies \boxed{DA=√(17)} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Perimeter}}{√(10)~~ + ~~√(13)~~ + ~~2~~ + ~~√(17)}~~ \approx ~~ 12.89`