Question

Find the perimeter of the parallelogram with these vertices.

(3.5), (-4. 2), (3.1), (-4. -2)
Give an exact answer (not a decimal approximation).
Simplify your answer as much as possible.

Answer 1

Check the picture below.

so we can say that two sides are "4" each in length, since opposite sides are equal, let's find how long the slanted sides are.

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-4}~,~\stackrel{y_1}{2})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{5})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ d=√([3 - (-4)]^2 + [5 - 2]^2)\implies d=√((3+4)^2+3^2) \\\\\\ d=√(49+9)\implies d=√(58) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Perimeter}}{4~~ + ~~4~~ + ~~√(58)~~ + ~~√(58)\implies 8+2√(58)}`