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
[tex]d= \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
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 = [tex]\sqrt{(-2-2)^{2}+(3-4)^{2}} = \sqrt{16+1} = sqrt{17}[/tex]
Length, BC = [tex]\sqrt{(1+2)^{2}+(-9-3)^{2}} = \sqrt{9+144} = 3 sqrt{17}[/tex]
Now, Area of rectangle = Length * Breadth = AB * BC = √17 * 3√17 = 3 *17 = 51
∴ The area of the given rectangle is 51
