Question

Find the perimeter of the polygon with the vertices 01 - 3, 2), R(1,2), (1, - 2), and 77 - 3. - 2).The perimeter isunits.

Answer 1

Approximately 30.47 units

To find the Perimeter of this polygon, we can find by calculating the distance between each point

Considering the points are:

1 (3,2) R (1,2) (7,7) and (-3,-2)

1) Let's calculate the distance between each of them, using the formula of the distance derived from the Pythagorean Theorem.

d1 = (3,2) and (1,2)

d_2 =(1,2) and (7,7)

d_3= (7,7) and (-3,-2)

d_4= (-3,-2) and (3,2)

`\begin{gathered} d_{}=\sqrt{(x_(_2-)x_{1\text{ }})^2+(y_2-y_1)^2^{_{}}} \\ d_(_1=)√((1-3)^2+(2-2)^2)=2 \\ d_2=√((7-1)^2+(7-2)^2)=√(61) \\ d_3=√((-3-7)^2+(-2-7)^2)=√(181) \\ d_4\text{ =}√((3+3)^2+(2+2)^2)=2√(13) \end{gathered}`

2) Since we have four points then let's consider them as our vertices, and add those line segments do calculate its Perimeter (2P)

`2P\text{ = 2 +}√(61)+2√(13)+√(181)\text{ }\approx\text{ 30.47}`

Notice that for those radicals are not perfect squares they are irrational so approximating these we have.