Given vertices of the rectangle :
(-2,8)
(4,9)
(6,-3) and (0,-4)
Length of the rectangle is the distance of (-2,8) to (4,9).
[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]=\sqrt{\left(4-\left(-2\right)\right)^2+\left(9-8\right)^2}[/tex]
[tex]=\sqrt{37}[/tex]
Width of the rectangle is the distance of (4,9) and (6,-3).
[tex]=\sqrt{\left(6-4\right)^2+\left(-3-9\right)^2}[/tex]
[tex]=2\sqrt{37}[/tex]
Area of the rectangle = Length × Width
= [tex]\sqrt{37}\times 2\sqrt{37}[/tex]
= 2 × 37
= 74.
