Answer:
The cost of fencing is $670.5.
Step-by-step explanation:
It is given that the cost of fencing is $1.30 per yard.
From the given figure it is clear that the M(-4,2), N(1,4), O(4,4), P(4,0).
Distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Using distance formula, we get
[tex]MN=\sqrt{\left(1-\left(-4\right)\right)^2+\left(4-2\right)^2}=\sqrt{29}[/tex]
[tex]NO=\sqrt{\left(4-1\right)^2+\left(4-4\right)^2}=3[/tex]
[tex]OP=\sqrt{\left(4-4\right)^2+\left(0-4\right)^2}=4[/tex]
[tex]MP=\sqrt{\left(4-\left(-4\right)\right)^2+\left(0-2\right)^2}=2\sqrt{17}[/tex]
The perimeter of the given polygon is
[tex]Perimeter=MN+NO+OP+MP[/tex]
[tex]Perimeter=\sqrt{29}+3+4+2\sqrt{17}[/tex]
[tex]Perimeter\approx 20.63[/tex]
The perimeter of the given polygon is 20.63 units.
It is given that 1 units = 25 yards.
[tex]20.63\text{ units}=20.63\times 25\text{ yards}[/tex]
[tex]20.63\text{ units}=515.75\text{ yards}[/tex]
Cost of fencing = $1.30 per yard
[tex]cost=670.475\approx 670.5[/tex]
Therefore the cost of fencing is $670.5.