The area of a rectangle is the product of its dimensions. The area of rectangle BCEF is 16 square units
Given that:
[tex]B = (0,3)[/tex]
[tex]C = (4,-1)[/tex]
[tex]E =(2,-3)[/tex]
[tex]F = (-2,1)[/tex]
Refer to attachment for the missing figure
The area of a rectangle is:
[tex]Area= Length \times Width[/tex]
The length of the rectangle can be represented as: BC or FE
The width of the rectangle can be represented as: BF or CE
The lengths of these sides can be calculated using distance formula
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
So, we have:
[tex]BC = \sqrt{(4- 0)^2 + (-1- 3)^2}[/tex]
[tex]BC = \sqrt{32}[/tex] ------ This represents length
[tex]BF = \sqrt{(-2- 0)^2 + (1- 3)^2}[/tex]
[tex]BF = \sqrt{8}[/tex] ---- This represents width
The area is:
[tex]Area= Length \times Width[/tex]
[tex]Area = BF \times BC[/tex]
[tex]Area = \sqrt{32} \times \sqrt{8}[/tex]
[tex]Area = \sqrt{32 \times 8}[/tex]
[tex]Area = \sqrt{256}[/tex]
[tex]Area = 16[/tex]
Hence, the area of the rectangle is 16 square units
Read more about area on a coordinate plane at;
https://brainly.com/question/3903921
