Answer:
The cost of fencing is $670.5.
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=√((x_2-x_1)^2+(y_2-y_1)^2)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/jq23b7gn8a5hqb5oj8gmcxlbivj810cso4.png)
Using distance formula, we get
![MN=√(\left(1-\left(-4\right)\right)^2+\left(4-2\right)^2)=√(29)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/v70wekznefawn3tcuqoi6u33m8ayxf7qs2.png)
![NO=√(\left(4-1\right)^2+\left(4-4\right)^2)=3](https://img.qammunity.org/2020/formulas/mathematics/middle-school/8ejryvgsidoe6p6vdjoqqczxpao86ycmxo.png)
![OP=√(\left(4-4\right)^2+\left(0-4\right)^2)=4](https://img.qammunity.org/2020/formulas/mathematics/middle-school/sp65vzyyx1n5tcrug50iiw53rysdflirls.png)
![MP=√(\left(4-\left(-4\right)\right)^2+\left(0-2\right)^2)=2√(17)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/8383o9624pfg7cyvvy0gfgs45kueyz2vgd.png)
The perimeter of the given polygon is
![Perimeter=MN+NO+OP+MP](https://img.qammunity.org/2020/formulas/mathematics/middle-school/ec3fbp02i0r5fec2pcx8j40ic82nxcojyd.png)
![Perimeter=√(29)+3+4+2√(17)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/rel84zjlfdrl2xqh0s3ffloyecq50zpyvn.png)
![Perimeter\approx 20.63](https://img.qammunity.org/2020/formulas/mathematics/middle-school/crkwyz1fjuwqp4d9lkwjgejpqm8y18oa6m.png)
The perimeter of the given polygon is 20.63 units.
It is given that 1 units = 25 yards.
![20.63\text{ units}=20.63* 25\text{ yards}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/qh7u6t44hhgmgaj11jdzojrr3ooiv5r2tt.png)
![20.63\text{ units}=515.75\text{ yards}](https://img.qammunity.org/2020/formulas/mathematics/middle-school/j095fsu10v7ai085xyysh2z9ygik8axed4.png)
Cost of fencing = $1.30 per yard
![cost=670.475\approx 670.5](https://img.qammunity.org/2020/formulas/mathematics/middle-school/l6awn4usg9cuz8pccl8dokjzvommf4v1cs.png)
Therefore the cost of fencing is $670.5.