Carlos has a garden with coordinates a(3, 0), b(5,5), c(11,5) and d(9,0), where each unit equals one foot.

part a: select all of the dimensions of the garden.
a. 6.0 ft
b. 5.4 ft
c. 5.0 ft.
d. 4.5 ft.
e. 11.0 ft.

part b: if carlos decides to fence in the garden, how much fencing material should be purchase? round to the nearest tenth if needed.

part c: what is the most precise name for the shape of the fence?
a. parallelogram
b. rectangle
c. square
d. quadrilateral

The amount of fencing needed is 22.8 ft. Since the fence has four sides, hence it is a quadrilateral.

The distance between two points A(x₁, y₁) and B(x₂, y₂) is given by:

Given the coordinates A(3, 0), B(5,5), C(11,5) and D(9,0). Hence:

The amount of fencing = AB + BC + CD + AD = 5.4 + 6.0 + 5.4 + 6.0 = 22.8 ft.

Since the fence has four sides, hence it is a quadrilateral.

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Part A:  A. 6.0 ft; B. 5.4 ft

Part B:  22.8 ft

Part C:  A. Parallelogram

Part A

The distance formula for the length between two points (x1, y1) and (x2, y2) is ...

  d = √((x2-x1)^2 +(y2-y1)^2)

For segment AD, the points are A(3, 0) and D(9, 0), so the distance is ...

  AD = √((9-3)^2 +(0-0)^2) = 6

For segment AB, the points are A(3, 0) and B(5, 5), so the distance is ...

  AB = √((5-3)^2 +(5-0)^2) = √29 ≈ 5.3852 ≈ 5.4

A plot of the points reveals the figure to be a parallelogram, so these are the only two dimensions of interest.

Side lengths of the garden fence are 6.0 ft and 5.4 ft.

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Part B

There are two sides of the garden of each length, so the total perimeter length is ...

   P = 2(6.0 +5.4) = 2·11.4 = 22.8 . . . feet

Carlos needs 22.8 feet of fencing material.

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Part C

As we discovered in Part A when we plotted the points, the shape is a parallelogram.

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