Answer:
The area of the rectangle is 60 square units.
Step-by-step explanation:
The given figure represents a rectangle with vertices (-5,2), (-7,-2), (5,-8) and (7,-4).
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Find the distance between (-5,2) and (7,-4), to calculate the length of the rectangle.
[tex]l=\sqrt{(7-(-5))^2+(-4-2)^2}=\sqrt{(12)^2+(-6)^2} =\sqrt{144+36}=\sqrt{180}[/tex]
Find the distance between (7,-4) and (5,-8), to calculate the width of the rectangle.
[tex]w=\sqrt{(5-7)^2+(-8-(-4))^2}=\sqrt{(-2)^2+(-4)^2}=\sqrt{4+16}=\sqrt{20}[/tex]
The area of rectangle is
[tex]A=l\times w[/tex]
[tex]A=\sqrt{180}\times \sqrt{20}[/tex]
[tex]A=\sqrt{3600}[/tex]
[tex]A=60[/tex]
Therefore the area of the rectangle is 60 square units.
