Answer:
Using distance(D) formula for two points is given by:
[tex]D = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
From the given figure:
The coordinates of the quadrilateral ABCD are:
A(-3, 2), B(4, 2), C(3, -3) and D(-3, -3)
For A(-3, 2) and B(4, 2)
using formula we have;
[tex]AB= \sqrt{(-3-4)^2+(2-2)^2}[/tex]
⇒[tex]AB= \sqrt{(-7)^2+(0)^2}[/tex]
⇒[tex]AB= \sqrt{49} =7[/tex] units
Similarly;
For B(4, 2) and C(3, -3)
[tex]BC= \sqrt{(4-3)^2+(2-(-3))^2}[/tex]
⇒[tex]BC= \sqrt{(1)^2+(5)^2}[/tex]
⇒[tex]BC= \sqrt{1+25}=\sqrt{26}[/tex] units.
For C(3, -3) and D(-3, -3)
[tex]CD= \sqrt{(3-(-3))^2+(-3-(-3))^2}[/tex]
⇒[tex]CD= \sqrt{(6)^2+(0)^2}[/tex]
⇒[tex]CD= \sqrt{36+0}=\sqrt{36}=6[/tex] units.
For A(-3, 2) and D(-3, -3)
[tex]AD= \sqrt{(-3-(-3))^2+(2-(-3))^2}[/tex]
⇒[tex]AD= \sqrt{0+25}=\sqrt{25}=5[/tex] units.
Perimeter is equal to the sum of all the sides of quadrilateral ABCD:
Perimeter = AB+BC+CD+AD
then;
[tex]\text{Perimeter} = 7+\sqrt{26}+6+5 = 18+\sqrt{26}[/tex] units
Therefore, the perimeter of quadrilateral ABCD is, [tex] 18+\sqrt{26}[/tex] units
