Answer:
The perimeter is about 16.94 units.
Step-by-step explanation:
we know that
The perimeter of the polygon is the sum of its length sides
so
[tex]P=AB+BC+CD+DE+EF+FA[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Find the distance AB
A(0,4),B(2,0)
substitute in the formula
[tex]d=\sqrt{(0-4)^{2}+(2-0)^{2}}[/tex]
[tex]dAB=\sqrt{20}=4.47\ units[/tex]
step 2
Find the distance BC
B(2,0),C(2,-2)
substitute in the formula
[tex]d=\sqrt{(-2-0)^{2}+(2-2)^{2}}[/tex]
[tex]dBC=2\ units[/tex]
step 3
Find the distance CD
C(2,-2),D(0,-2)
substitute in the formula
[tex]d=\sqrt{(-2+2)^{2}+(0-2)^{2}}[/tex]
[tex]dCD=2\ units[/tex]
step 4
Find the distance DE
D(0,-2),E(-2,2)
substitute in the formula
[tex]d=\sqrt{(2+2)^{2}+(-2-0)^{2}}[/tex]
[tex]dDE=\sqrt{20}=4.47\ units[/tex]
step 5
Find the distance EF
E(-2,2),F(-2,4)
substitute in the formula
[tex]d=\sqrt{(4-2)^{2}+(-2+2)^{2}}[/tex]
[tex]dE.F=2\ units[/tex]
step 6
Find the distance FA
F(-2,4),A(0,4)
substitute in the formula
[tex]d=\sqrt{(4-4)^{2}+(0+2)^{2}}[/tex]
[tex]dFA=2\ units[/tex]
step 7
Find the perimeter
[tex]P=4.47+2+2+4.47+2+2=16.94\ units[/tex]
