Question

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

Answer 1

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=\sqrt{(8+2)^2+(3+1)^2}$$AB=\sqrt{116}=2\sqrt{29}$$BC=\sqrt{(-5+2)^2+(3+1)^2}$$BC=\sqrt{9+16}$$BC=\sqrt{25}=5$$AE=\sqrt{(0+8)^2+(-5-3)^2}$$AE=\sqrt{64+64}$$AE=\sqrt{128}=8\sqrt{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