Answer:
34 square units
Explanation:
In any rectangle, each two opposite sides are equal
This means that, in the given rectangle:
AB = CD and AD = BC
Area of the rectangle is the product of its dimensions (length and width)
This means that:
Area of ABCD = AB × BC
1- getting the side length:
To get the side length, we will use the distance formula:
[tex]D = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2}[/tex]
For AB, we have:
A = (-1,4) which means that x₁ = -1 and y₁ = 4
B = (3,3) which means that x₂ = 3 and y₂ = 3
Substitute in the equation:
[tex]AB = \sqrt{(3-(-1))^2+(3-4)^2} = \sqrt{17}[/tex] units
For BC, we have:
B = (3,3) which means that x₁ = 3 and y₁ = 3
C = (1,-5) which means that x₂ = 1 and y₂ = -5
Substitute in the equation:
[tex]BC = \sqrt{(1-3)^2+(-5-3)^2} = 2\sqrt{17}[/tex] units
2- getting the area:
Area of ABCD = AB × BC
Area of ABCD = [tex]\sqrt{17} * 2\sqrt{17} = 34[/tex] square units
Hope this helps :)
