Answer:
Option (4)
Step-by-step explanation:
Coordinates of the vertices of the given trapezoid,
A(-9, 4), B(-4, -3), C(2, -4), D(9, 1) and E(-3, 3)
Perimeter of ABCD = length of AB + length of BC + length of CD + length of DA
Length of AB = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
= [tex]\sqrt{(-9+4)^2+(4+3)^2}[/tex]
= [tex]\sqrt{25+49}[/tex]
= [tex]\sqrt{74}[/tex]
Length of BC = [tex]\sqrt{(-4-2)^2+(-3+4)^2}[/tex]
= [tex]\sqrt{36+1}[/tex]
= [tex]\sqrt{37}[/tex]
Length of CD = [tex]\sqrt{(2-9)^2+(-4-1)^2}[/tex]
= [tex]\sqrt{49+25}[/tex]
= [tex]\sqrt{74}[/tex]
Length of DA = [tex]\sqrt{(-9-9)^2+(4-1)^2}[/tex]
= [tex]\sqrt{324+9}[/tex]
= [tex]\sqrt{333}[/tex]
Perimeter of ABCD = [tex]\sqrt{74}+\sqrt{37}+\sqrt{74}+\sqrt{333}[/tex]
= [tex]\sqrt{74}+\sqrt{37}+\sqrt{74}+3\sqrt{37}[/tex]
= [tex]4\sqrt{37}+2\sqrt{74}[/tex]
Therefore, Option (4) will be the answer.
