Answer: The area of the given rectangle is 20 sq. units.
Step-by-step explanation: We are given to find the area of a rectangle with the co-ordinates of the vertices as (-8-2), (-3-2), (-3-6) and (-8-6).
Let the co-ordinates of vertices of the given rectangle be A(-8-2), B(-3-2), C(-3-6) and D(-8-6).
Then, the lengths of the sides AB, BC, CD and DA are calculated using distance formula as follows:
[tex]AB=\sqrt{(-3+8)^2+(-2+2)^2}=\sqrt{25}=5~\textup{units},\\\\BC=\sqrt{(-3+3)^2+(-6+2)^2}=\sqrt{16}=4~\textup{units},\\\\CD=\sqrt{(-8+3)^2+(-6+6)^2}=\sqrt{25}=5~\textup{units},\\\\DA=\sqrt{(-8+8)^2+(-2+6)^2}=\sqrt{16}=4~\textup{units}.[/tex]
So, the length of the rectangle is 5 units and its breadth is 4 units.
We know that the area of a rectangle is the product of its length and breadth, so the area of the given rectangle will be
[tex]A=5\times4=20~\textup{sq units.}[/tex]
Thus, the area of the given rectangle is 20 sq. units.
