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:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Using distance formula, we get
![MN=\sqrt{\left(1-\left(-4\right)\right)^2+\left(4-2\right)^2}=\sqrt{29}](https://tex.z-dn.net/?f=MN%3D%5Csqrt%7B%5Cleft%281-%5Cleft%28-4%5Cright%29%5Cright%29%5E2%2B%5Cleft%284-2%5Cright%29%5E2%7D%3D%5Csqrt%7B29%7D)
![NO=\sqrt{\left(4-1\right)^2+\left(4-4\right)^2}=3](https://tex.z-dn.net/?f=NO%3D%5Csqrt%7B%5Cleft%284-1%5Cright%29%5E2%2B%5Cleft%284-4%5Cright%29%5E2%7D%3D3)
![OP=\sqrt{\left(4-4\right)^2+\left(0-4\right)^2}=4](https://tex.z-dn.net/?f=OP%3D%5Csqrt%7B%5Cleft%284-4%5Cright%29%5E2%2B%5Cleft%280-4%5Cright%29%5E2%7D%3D4)
![MP=\sqrt{\left(4-\left(-4\right)\right)^2+\left(0-2\right)^2}=2\sqrt{17}](https://tex.z-dn.net/?f=MP%3D%5Csqrt%7B%5Cleft%284-%5Cleft%28-4%5Cright%29%5Cright%29%5E2%2B%5Cleft%280-2%5Cright%29%5E2%7D%3D2%5Csqrt%7B17%7D)
The perimeter of the given polygon is
![Perimeter=MN+NO+OP+MP](https://tex.z-dn.net/?f=Perimeter%3DMN%2BNO%2BOP%2BMP)
![Perimeter=\sqrt{29}+3+4+2\sqrt{17}](https://tex.z-dn.net/?f=Perimeter%3D%5Csqrt%7B29%7D%2B3%2B4%2B2%5Csqrt%7B17%7D)
![Perimeter\approx 20.63](https://tex.z-dn.net/?f=Perimeter%5Capprox%2020.63)
The perimeter of the given polygon is 20.63 units.
It is given that 1 units = 25 yards.
![20.63\text{ units}=20.63\times 25\text{ yards}](https://tex.z-dn.net/?f=20.63%5Ctext%7B%20units%7D%3D20.63%5Ctimes%2025%5Ctext%7B%20yards%7D)
![20.63\text{ units}=515.75\text{ yards}](https://tex.z-dn.net/?f=20.63%5Ctext%7B%20units%7D%3D515.75%5Ctext%7B%20yards%7D)
Cost of fencing = $1.30 per yard
![cost=670.475\approx 670.5](https://tex.z-dn.net/?f=cost%3D670.475%5Capprox%20670.5)
Therefore the cost of fencing is $670.5.