Answer:
Perimeter of the Quadrilateral=20.78
Step-by-step explanation:
Perimeter of the Quadrilateral= AB+BC+CD+AD
Finding the sides of the quadrilateral using the Distance formula:
A(-3,0), B(2,4), C(3,1) and D(-4,-3)
[tex]AB=\sqrt{(2-(-3))^2+(4-0)^2}\\\\ =\sqrt{(2+3)^2+4^2}\\\\ =\sqrt{5^2+4^2} \\\\=\sqrt{25+16}\\\\ =\sqrt{41}\\[/tex]
[tex]=6.40[/tex]
BC=
[tex]\sqrt{(3-2)^2+(1-4)^2} \\\\=\sqrt{1^2+(-3)^2} \\\\=\sqrt{1+9}\\\\ =\sqrt{10}[/tex]
[tex]=3.16[/tex]
[tex]CD=\sqrt{(-4-3)^2+(-3-1)^2} \\\\=\sqrt{(-7)^2+(-4)^2} \\\\=\sqrt{49+16}\\\\=\sqrt{65}\\\\ =8.06[/tex]
[tex]AD=\sqrt{(-4-(-3))^2+(-3-0)^2} \\\\=\sqrt{(-4+3)^2+(-3)^2} \\\\=\sqrt{(-1)^2+(-3)^2} \\\\=\sqrt{1+9}\\\\=\sqrt{10} \\\\ =3.16[/tex]
Perimeter of the quadrilateral= AB+BC+CD+AD
=6.40+3.16+8.06+3.16
=20.78
