The area of a shape is the amount of space it can occupy.
The area of the polygon is [tex]8+ \sqrt 2[/tex] square units
Given
[tex]A=(0,5)[/tex]
[tex]B =(2,5)[/tex]
[tex]C =(2,3)[/tex]
[tex]D = (3,2)[/tex]
[tex]E = (1,2)[/tex]
[tex]F = (0,3)[/tex]
[tex]G = (-4,3)[/tex]
First, we plot the points (see attachment)
From the attached image, the polygon can be into split to several shapes as follows:
The area of a shape is the amount of space it can occupy.
The area of the polygon is [tex]8+ \sqrt 2[/tex] square units
Given
[tex]A=(0,5)[/tex]
[tex]B =(2,5)[/tex]
[tex]C =(2,3)[/tex]
[tex]D = (3,2)[/tex]
[tex]E = (1,2)[/tex]
[tex]F = (0,3)[/tex]
[tex]G = (-4,3)[/tex]
First, we plot the points (see attachment)
From the attached image, the polygon can be into split to several shapes as follows:
The area of the square is:
[tex]Area = Length^2[/tex]
using the following distance formula
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]
So, we have:
[tex]A\ F = \sqrt{(0- 0)^2 + (5- 3)^2}[/tex]
[tex]A\ F = \sqrt{4}[/tex]
[tex]A\ F = 2[/tex]
So, we have:
[tex]Area =2^2[/tex]
[tex]Area = 4[/tex]
The area of the triangle is:
[tex]Area= 0.5 \times Base \times Height[/tex]
Where
[tex]Height = A\ F =2[/tex]
[tex]Base =FG[/tex]
Side length FG is calculated as follows:
[tex]FG = \sqrt{(0 --4)^2 + (3 -3)^2}[/tex]
[tex]FG = \sqrt{16}[/tex]
[tex]FG =4[/tex]
So, we have:
[tex]Area= 0.5 \times Base \times Height[/tex]
[tex]Area = 0.5 \times 2 \times 4[/tex]
[tex]Area =4[/tex]
The area of the rhombus is:
[tex]Area= \frac{1}{2} (FD \times CE)[/tex]
Where:
[tex]FD = \sqrt{(1 - 3)^2 + (2 - 2)^2}[/tex]
[tex]FD = \sqrt{4}[/tex]
[tex]FD = 2[/tex]
[tex]CE = \sqrt{(2 -1)^2 + (3 -2)^2}[/tex]
[tex]CE = \sqrt{2}[/tex]
So, we have:
[tex]Area= \frac{1}{2} (FD \times CE)[/tex]
[tex]Area = \frac 12(2 \times \sqrt 2)[/tex]
[tex]Area = \sqrt 2[/tex]
So, the area of the shape is the sum of the three areas;
[tex]Area = 4 + 4 + \sqrt 2[/tex]
[tex]Area = 8+ \sqrt 2[/tex]
Hence, the area of the polygon is [tex]8+ \sqrt 2[/tex] square units
Read more about areas at:
https://brainly.com/question/16418397
