Answer:
The area of a rectangle is 42 units ².
Step-by-step explanation:
As the diagram is given below.
Distance Formula
[tex]Distance\ formula = \sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
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)
[tex]AB = \sqrt{(11-4)^{2}+(3-3)^{2}}[/tex]
[tex]AB = \sqrt{(7)^{2}+(0)^{2}}[/tex]
[tex]AB = \sqrt{49}[/tex]
[tex]\sqrt{49} =7[/tex]
AB = 7 units
As take B(11, 3) to C (11, 9).
[tex]BC = \sqrt{(11-11)^{2}+(9-3)^{2}}[/tex]
[tex]BC = \sqrt{(0)^{2}+(6)^{2}}[/tex]
[tex]BC = \sqrt{36}[/tex]
[tex]\sqrt{36} =6[/tex]
BC = 6 units
As take C (11, 9) toD (4, 9).
[tex]CD = \sqrt{(4-11)^{2}+(9- 9)^{2}}[/tex]
[tex]CD = \sqrt{(7)^{2}+(0)^{2}}[/tex]
[tex]CD = \sqrt{49}[/tex]
[tex]\sqrt{49} =7[/tex]
CD = 7 units
As take D (4, 9) to A (4, 3)
[tex]DA = \sqrt{(4-4)^{2}+(3-9)^{2}}[/tex]
[tex]DA = \sqrt{(0)^{2}+(-6)^{2}}[/tex]
[tex]DA = \sqrt{36}[/tex]
[tex]\sqrt{36} =6[/tex]
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.
