Question

In Exercises 5-8, find the perimeter and area of the polygon with the given vertices.

5. X(2, 4), Y(0, -2), Z (2,-2)

Answer 1

Check the picture below.

as we can see in the picture, the lengths for YZ and ZX are very straight, let's get the side YX

`~~~~~~~~~~~~\textit{distance between 2 points} \\\\ Y(\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\qquad X(\stackrel{x_2}{2}~,~\stackrel{y_2}{4})\qquad \qquad d = √(( x_2- x_1)^2 + ( y_2- y_1)^2) \\\\\\ YX=√([2 - 0]^2 + [4 - (-2)]^2)\implies YX=√(2^2+(4+2)^2) \\\\\\ YX=√(4+6^2)\implies YX=√(40) \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Perimeter}}{2~~+~~6~~+~~√(40)~~\approx~~14.32} ~\hfill \stackrel{\textit{\Large Area}}{\cfrac{1}{2}(2)(6)\implies 6}`