Answer:
Therefore Area of Rectangle is 50 unit².
Step-by-step explanation:
Given:
Let the vertices of a Rectangle be
A ( -1 , 7)
B ( 4 , -3)
C ( 0 , -5)
D ( -5 ,5)
To Find:
Area of Rectangle ABCD = ?
Solution:
First we will find the Length and Width of Rectangle by Distance Formula ,
[tex]l(AB) = \sqrt{((x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2} )}[/tex]
Substituting the values we get
[tex]l(AB) = \sqrt{((4-(-1))^{2}+(-3-7)^{2} )}[/tex]
[tex]l(AB) = \sqrt{((5)^{2}+(-10)^{2} )}\\l(AB)=\sqrt{125}=5\sqrt{5}\ unit[/tex]
Similarly for BC we will have,
[tex]l(BC) = \sqrt{((0-4)^{2}+(-5-(-3))^{2} )}\\l(BC)=\sqrt{20}=2\sqrt{5}\ unit[/tex]
Now
[tex]Length=AB =5\sqrt{5}\ unit\\Width=BC=2\sqrt{5}\ unit[/tex]
Now Area of Rectangle is given by
[tex]\textrm{Area of Rectangle}=Length\times Width[/tex]
Substituting the values we get
[tex]\textrm{Area of Rectangle ABCD}=5\sqrt{5}\times 2\sqrt{5}=10\times 5=50\ unit^{2}[/tex]
Therefore Area of Rectangle is 50 unit².
