Answer:
The area of a rectangle is 42 units ².
Step-by-step explanation:
As the diagram is given below.
Distance Formula
![Distance\ formula = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}](https://tex.z-dn.net/?f=Distance%5C%20formula%20%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)
As the rectangle with vertices at A (4, 3), B(11, 3),C (11, 9), and D (4, 9).
Take A (4, 3) to B(11, 3)
![AB = \sqrt{(11-4)^{2}+(3-3)^{2}}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%2811-4%29%5E%7B2%7D%2B%283-3%29%5E%7B2%7D%7D)
![AB = \sqrt{(7)^{2}+(0)^{2}}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B%287%29%5E%7B2%7D%2B%280%29%5E%7B2%7D%7D)
![AB = \sqrt{49}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7B49%7D)
![\sqrt{49} =7](https://tex.z-dn.net/?f=%5Csqrt%7B49%7D%20%3D7)
AB = 7 units
As take B(11, 3) to C (11, 9).
![BC = \sqrt{(11-11)^{2}+(9-3)^{2}}](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B%2811-11%29%5E%7B2%7D%2B%289-3%29%5E%7B2%7D%7D)
![BC = \sqrt{(0)^{2}+(6)^{2}}](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B%280%29%5E%7B2%7D%2B%286%29%5E%7B2%7D%7D)
![BC = \sqrt{36}](https://tex.z-dn.net/?f=BC%20%3D%20%5Csqrt%7B36%7D)
![\sqrt{36} =6](https://tex.z-dn.net/?f=%5Csqrt%7B36%7D%20%3D6)
BC = 6 units
As take C (11, 9) toD (4, 9).
![CD = \sqrt{(4-11)^{2}+(9- 9)^{2}}](https://tex.z-dn.net/?f=CD%20%3D%20%5Csqrt%7B%284-11%29%5E%7B2%7D%2B%289-%209%29%5E%7B2%7D%7D)
![CD = \sqrt{(7)^{2}+(0)^{2}}](https://tex.z-dn.net/?f=CD%20%3D%20%5Csqrt%7B%287%29%5E%7B2%7D%2B%280%29%5E%7B2%7D%7D)
![CD = \sqrt{49}](https://tex.z-dn.net/?f=CD%20%3D%20%5Csqrt%7B49%7D)
![\sqrt{49} =7](https://tex.z-dn.net/?f=%5Csqrt%7B49%7D%20%3D7)
CD = 7 units
As take D (4, 9) to A (4, 3)
![DA = \sqrt{(4-4)^{2}+(3-9)^{2}}](https://tex.z-dn.net/?f=DA%20%3D%20%5Csqrt%7B%284-4%29%5E%7B2%7D%2B%283-9%29%5E%7B2%7D%7D)
![DA = \sqrt{(0)^{2}+(-6)^{2}}](https://tex.z-dn.net/?f=DA%20%3D%20%5Csqrt%7B%280%29%5E%7B2%7D%2B%28-6%29%5E%7B2%7D%7D)
![DA = \sqrt{36}](https://tex.z-dn.net/?f=DA%20%3D%20%5Csqrt%7B36%7D)
![\sqrt{36} =6](https://tex.z-dn.net/?f=%5Csqrt%7B36%7D%20%3D6)
DA = 6 units
Thus
AB = DC= 7 units
AD = BC = 6 units
Formula
Area of rectangle = Length × Breadth
Length = 7 units
Breadth = 6 units
Put value in the above
Area of rectangle = 7 × 6
= 42 units ²
Therefore the area of a rectangle is 42 units ².