Question

calculator
the coordinates of the vertices of a polygon are (-5, 1), (-1, 3), (2, 3), (2, -2), and (-3, -1)
what is the perimeter of the polygon?
enter your answer as a decimal, rounded to the nearest tenth of a unit, in the box.
□ units

Explanation:

Step1: List vertices in order

Vertices: $A(-5,1)$, $B(-1,3)$, $C(2,3)$, $D(2,-2)$, $E(-3,-1)$, back to $A(-5,1)$

Step2: Calculate AB length

Distance formula: $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$AB=\sqrt{(-1+5)^2+(3-1)^2}=\sqrt{16+4}=\sqrt{20}\approx4.472$

Step3: Calculate BC length

$BC=\sqrt{(2+1)^2+(3-3)^2}=\sqrt{9+0}=3$

Step4: Calculate CD length

$CD=\sqrt{(2-2)^2+(-2-3)^2}=\sqrt{0+25}=5$

Step5: Calculate DE length

$DE=\sqrt{(-3-2)^2+(-1+2)^2}=\sqrt{25+1}=\sqrt{26}\approx5.099$

Step6: Calculate EA length

$EA=\sqrt{(-5+3)^2+(1+1)^2}=\sqrt{4+4}=\sqrt{8}\approx2.828$

Step7: Sum all lengths

Total perimeter: $4.472+3+5+5.099+2.828\approx20.4$

Answer:

20.4