Answer:
The area of the rectangle <em>TOUR</em> is 80.00 unit².
Step-by-step explanation:
The area of a rectangle is computed using the formula:
![Area\ of\ a\ Rectangle=length\times width](https://tex.z-dn.net/?f=Area%5C%20of%5C%20a%5C%20Rectangle%3Dlength%5Ctimes%20width)
Since the dimensions of the rectangle are not provided we can compute the dimensions using the distance formula for two points.
The distance formula using the two point is:
![distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}](https://tex.z-dn.net/?f=distance%3D%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E%7B2%7D%2B%28y_%7B2%7D-y_%7B1%7D%29%5E%7B2%7D%7D)
Considering the rectangle <em>TOUR</em> the area formula will be:
Area of Rectangle <em>TOUR</em> = <em>TO × OU</em>
The co-ordinates of the four vertices of a triangle are:
T = (-8, 0), O = (4, 4), U = (6, -2) and R = (-6, -6)
Compute the distance between the vertices <em>T</em> and <em>O</em> as:
![TO=\sqrt{(4-(-8))^{2}+(4-0)^{2}}\\=\sqrt{12^{2}+4^{2}} \\=\sqrt{160} \\=4\sqrt{10}](https://tex.z-dn.net/?f=TO%3D%5Csqrt%7B%284-%28-8%29%29%5E%7B2%7D%2B%284-0%29%5E%7B2%7D%7D%5C%5C%3D%5Csqrt%7B12%5E%7B2%7D%2B4%5E%7B2%7D%7D%20%5C%5C%3D%5Csqrt%7B160%7D%20%5C%5C%3D4%5Csqrt%7B10%7D)
Compute the distance between the vertices <em>O </em>and <em>U</em> as:
![OU=\sqrt{(6-4)^{2}+(-2-4)^{2}}\\=\sqrt{2^{2}+6^{2}} \\=\sqrt{40} \\=2\sqrt{10}](https://tex.z-dn.net/?f=OU%3D%5Csqrt%7B%286-4%29%5E%7B2%7D%2B%28-2-4%29%5E%7B2%7D%7D%5C%5C%3D%5Csqrt%7B2%5E%7B2%7D%2B6%5E%7B2%7D%7D%20%5C%5C%3D%5Csqrt%7B40%7D%20%5C%5C%3D2%5Csqrt%7B10%7D)
Compute the area of rectangle TOUR as follows:
![Area\ of\ TOUR=TO\times OU\\=4\sqrt{10}\times 2\sqrt{10}\\=80\\\approx80.00 unit^{2}](https://tex.z-dn.net/?f=Area%5C%20of%5C%20TOUR%3DTO%5Ctimes%20OU%5C%5C%3D4%5Csqrt%7B10%7D%5Ctimes%202%5Csqrt%7B10%7D%5C%5C%3D80%5C%5C%5Capprox80.00%20unit%5E%7B2%7D)
Thus, the area of the rectangle <em>TOUR</em> is 80.00 unit².