Answer:
The area of the rectangle TOUR is 80.00 unit².
Step-by-step explanation:
The area of a rectangle is computed using the formula:
[tex]Area\ of\ a\ Rectangle=length\times width[/tex]
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:
[tex]distance=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
Considering the rectangle TOUR the area formula will be:
Area of Rectangle TOUR = TO × OU
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 T and O as:
[tex]TO=\sqrt{(4-(-8))^{2}+(4-0)^{2}}\\=\sqrt{12^{2}+4^{2}} \\=\sqrt{160} \\=4\sqrt{10}[/tex]
Compute the distance between the vertices O and U as:
[tex]OU=\sqrt{(6-4)^{2}+(-2-4)^{2}}\\=\sqrt{2^{2}+6^{2}} \\=\sqrt{40} \\=2\sqrt{10}[/tex]
Compute the area of rectangle TOUR as follows:
[tex]Area\ of\ TOUR=TO\times OU\\=4\sqrt{10}\times 2\sqrt{10}\\=80\\\approx80.00 unit^{2}[/tex]
Thus, the area of the rectangle TOUR is 80.00 unit².
