The vertices of the fence have been given as:
Point A: ( 4, -4)
Point B: (-4, -4)
Point C: (-4, 3)
Point D: (1, 3)
Point E: (1, -1)
Point F: (4, -1)
Planner wants to add a gate between A and F for which he will not put metal fencing on that side.
We have to calculate the total number of yards of metal fencing that will be needed; as follows:
Length AB:
[tex]AB=\sqrt{\left(-4+4\right)²+(-4-4)²}=\sqrt{-8^2}^=\sqrt{64}=8[/tex]
Length BC:
[tex]BC=\sqrt{\left(3+4\right)²+\left(-4+4\right)²}=\sqrt{7^2}=7[/tex]
Length CD:
[tex]CD=\sqrt{\left(3-3\right)²+\left(1+4\right)²}=\sqrt{5^2}=5[/tex]
Length DE:
[tex]DE=\sqrt{\left(-1-3\right)²+\left(1-1\right)²}=\sqrt{-4^2}=\sqrt{16}=4[/tex]
Length FE:
[tex]FE=\sqrt{\left(-1+1\right)²+\left(4-1\right)²}=\sqrt{3^2}=3[/tex]
Now, total number of yards of the fence =
AB + BC + CD + DE + FE
8 + 7 + 5 + 4 + 3 = 27 yards
ANSWER
27 yards
