Answer:
The area of the given rectangle is 51
Step-by-step explanation:
First we have to find the coordinates of the vertices of the rectangle.
Then the length and breadth of it using distance formula.
The distance d between points (x₁ , y₁) and (x₂ , y₂) is given by
![d= \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}](https://tex.z-dn.net/?f=d%3D%20%5Csqrt%7B%28x_%7B2%7D-x_%7B1%7D%29%5E%7B2%7D%2B%28y_%7B2%7D-y_%7B1%7D%29%5E%7B2%7D%7D)
Finally calculate the area of rectangle using the formula,
Area of rectangle = Length * Breadth
From the given graph, we get the coordinates of the rectangle as
A(2,4) , B(-2,3) , C(1,-9) , D(5,-8)
Breadth, AB = ![\sqrt{(-2-2)^{2}+(3-4)^{2}} = \sqrt{16+1} = sqrt{17}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-2-2%29%5E%7B2%7D%2B%283-4%29%5E%7B2%7D%7D%20%3D%20%5Csqrt%7B16%2B1%7D%20%3D%20sqrt%7B17%7D)
Length, BC = ![\sqrt{(1+2)^{2}+(-9-3)^{2}} = \sqrt{9+144} = 3 sqrt{17}](https://tex.z-dn.net/?f=%5Csqrt%7B%281%2B2%29%5E%7B2%7D%2B%28-9-3%29%5E%7B2%7D%7D%20%3D%20%5Csqrt%7B9%2B144%7D%20%3D%203%20sqrt%7B17%7D)
Now, Area of rectangle = Length * Breadth = AB * BC = √17 * 3√17 = 3 *17 = 51
∴ The area of the given rectangle is 51