Answer:
The perimeter of quadrilateral ABCD is 27.48 units
Step-by-step explanation:
we know that
The perimeter of quadrilateral ABCD is the sum of its four length sides
so
[tex]P=AB+BC+CD+AD[/tex]
we have
A(-5, 4),B(0,3),C(4,-1) and D(4,-5)
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the distance AB
Substitute in the formula
[tex]d=\sqrt{(3-4)^{2}+(0+5)^{2}}[/tex]
[tex]d=\sqrt{(-1)^{2}+(5)^{2}}[/tex]
[tex]AB=\sqrt{26}\ units[/tex]
Find the distance BC
Substitute in the formula
[tex]d=\sqrt{(-1-3)^{2}+(4-0)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(4)^{2}}[/tex]
[tex]BC=\sqrt{32}\ units[/tex]
Find the distance CD
Substitute in the formula
[tex]d=\sqrt{(-5+1)^{2}+(4-4)^{2}}[/tex]
[tex]d=\sqrt{(-4)^{2}+(0)^{2}}[/tex]
[tex]CD=4\ units[/tex]
Find the distance AD
Substitute in the formula
[tex]d=\sqrt{(-5-4)^{2}+(4+5)^{2}}[/tex]
[tex]d=\sqrt{(-9)^{2}+(9)^{2}}[/tex]
[tex]AD=\sqrt{162}\ units[/tex]
Find the perimeter
substitute the values
[tex]P=\sqrt{26}+\sqrt{32}+4+\sqrt{162}=27.48\ units[/tex]
see the attached figure to better understand the problem
