Apark planner is designing a dog park. he wants to use a metal fence to enclose a kennel at the dog park. the vertices of the fence are shown below. the units on the coordinate plane are yards.

point a(4, -4)
point b(-4. -4)
point c(-4, 3)
point d(1, 3)
point e (1, -1)
point f(4, -1)

the planner wants to add a gate between points a and f. he will not put metal fencing on that side. what is the total number of yards of metal fencing that will be needed for the kennel at the dog park?

27 yards of the metal fencing will be required.

Step-by-step explanation:

The given 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.

Length AB = √[(-4+4)² + (-4-4)²] = √(-8)² = √64 = 8

Length BC = √[(3+4)²+(-4+4)²] = √7² = 7

Length CD = √[(3-3)²+(1+4)²] = √5² = 5

Length DE = √[(-1-3)²+(1-1)²] = √(-4)² = √16 = 4

Length FE = √[(-1+1)²+(4-1)²] = √3² = 3

Now total number of yards of the fence = AB + BC + CD + DE + FE = 8 + 7 + 5 + 4 + 3 = 27 yards

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