Answer:
[tex]15.2\ units[/tex]
Step-by-step explanation:
step 1
Plot the vertices of the polygon to better understand the problem
we have
[tex]A(-2, 1). B(-3, 3), C(-1, 5), D(2, 4),E(2, 1)[/tex]
using a graphing tool
The polygon is a pentagon (the number of sides is 5)
see the attached figure
The perimeter is equal to
[tex]P=AB+BC+CD+DE+AE[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 2
Find the distance AB
[tex]A(-2, 1). B(-3, 3)[/tex]
substitute in the formula
[tex]d=\sqrt{(3-1)^{2}+(-3+2)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(-1)^{2}}[/tex]
[tex]d_A_B=\sqrt{5}=2.24\ units[/tex]
step 3
Find the distance BC
[tex]B(-3, 3), C(-1, 5)[/tex]
substitute in the formula
[tex]d=\sqrt{(5-3)^{2}+(-1+3)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(2)^{2}}[/tex]
[tex]d_B_C=\sqrt{8}=2.83\ units[/tex]
step 4
Find the distance CD
[tex]C(-1, 5), D(2, 4)[/tex]
substitute in the formula
[tex]d=\sqrt{(4-5)^{2}+(2+1)^{2}}[/tex]
[tex]d=\sqrt{(-1)^{2}+(3)^{2}}[/tex]
[tex]d_C_D=\sqrt{10}=3.16\ units[/tex]
step 5
Find the distance DE
[tex]D(2, 4),E(2, 1)[/tex]
substitute in the formula
[tex]d=\sqrt{(1-4)^{2}+(2-2)^{2}}[/tex]
[tex]d=\sqrt{(-3)^{2}+(0)^{2}}[/tex]
[tex]d_D_E=\sqrt{9}\ units[/tex]
[tex]d_D_E=3\ units[/tex]
step 6
Find the distance AE
[tex]A(-2, 1).E(2, 1)[/tex]
substitute in the formula
[tex]d=\sqrt{(1-1)^{2}+(2+2)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(4)^{2}}[/tex]
[tex]d_A_E=\sqrt{16}\ units[/tex]
[tex]d_A_E=4\ units[/tex]
step 7
Find the perimeter
[tex]P=AB+BC+CD+DE+AE[/tex]
substitute the values
[tex]P=2.24+2.83+3.16+3+4=15.23\ units[/tex]
Round to the nearest tenth of a unit
[tex]P=15.2\ units[/tex]
