Answer:
52
Step-by-step explanation:
Distance formula can be used to find the area of the square.
Recall that the area of a square is the side length squared or [tex]A=s^2[/tex]. Since the lengths of the square aren't parallel to x nor y axis, we can't count the number of units that one point is from the other.
Distance formula finds the distance between two points using their coordinate labels or,
[tex]\sqrt{(x_2-x_1)^2+(y_2+y_1)^2}[/tex].
Taking the coordinate pairs of points D and E, the length of DE or the side length (s) of the square is,
[tex]s=DE=\sqrt{(-5-1)^2+(1-(-3))^2}[/tex]
[tex]DE=\sqrt{(-5-1)^2+(1+3)^2}[/tex]
[tex]DE=\sqrt{36+16}=\sqrt{52}[/tex]
So, the area of the square shown is,
[tex]A=s^2=DE^2=(\sqrt{52} )^2=52[/tex]..
