Question

Polygon ABCDE is shown in the coordinate plane find the area of the figure

Answer 1

The area of the shaded region (Polygon ABCDE) on the graph is 48 square units.

To find the area of Polygon ABCDE on the graph, we can divide it into two smaller shapes: triangle ABE and rectangle BCDE.

Triangle ABE

The base of triangle ABE is 8 units (the difference between the x-coordinates of points A and E), and the height is 6 units (the difference between the y-coordinates of points A and B). Therefore, the area of triangle ABE is:

(1/2) * base * height = (1/2) * 8 * 6 = 24 square units

Rectangle BCDE

The base of rectangle BCDE is 6 units (the difference between the x-coordinates of points B and D), and the height is 4 units (the difference between the y-coordinates of points B and C). Therefore, the area of rectangle BCDE is:

base * height = 6 * 4 = 24 square units

Total area

The total area of Polygon ABCDE is the sum of the areas of triangle ABE and rectangle BCDE:

24 square units + 24 square units = 48 square units

Answer 2

Given the shown figure

Points

A( 8 , 3 )

B( - 2 , -1)

C( - 5 , 3)

D( -5 , -5)

E( 0, -5)

Segments

CD= 5+ 3 = 8

DE= 5

`AB=√((8+2)^2+(3+1)^2)`
`AB=√(116)=2√(29)`
`BC=√((-5+2)^2+(3+1)^2)`
`BC=√(9+16)`
`BC=√(25)=5`
`AE=√((0+8)^2+(-5-3)^2)`
`AE=√(64+64)`
`AE=√(128)=8√(2)`

we can separate the figure into 5 related figures as follows

then the area is the sum of

`A=(4*3)+(2*4)+(6)+(8)+(5.5)`
`A=39.5`

A=39.5u^2