Columbia Southern University Unit IV Geometry Garden Questions

Unit IV Assignment: Geometry GardenIn this assignment, you will be asked to find specific information related to the area and perimeter of a
garden you are designing.
Instructions: Imagine that you are landscaper who is designing a garden for your clients. The garden
must contain a fountain, a stone path, two flower beds, and a sprinkler system. The fountain, stone path,
and flower beds can be placed anywhere inside the garden. An example of a design is shown below.
Answer questions 1–7. Save all of your work to this template and submit it in Blackboard for grading.
Flower
Bed
Stone Path
Fountain
Flower
Bed
Part One: For questions 1–4, identify the dimensions of the garden and its components. You can select
any whole number for the dimensions of each component; however, the dimensions must fit the criteria
outlined in the questions below. All dimensions should be given in feet.
1. What is the length and width of the garden? Select any whole number between 30–70 feet for the
length and 20–50 feet for the width.
Length of Garden:
Width of Garden:
?? ft.
?? ft.
2. A circular fountain will be included inside the garden. What is the diameter of the fountain? Select any
whole number between 3–5 feet.
Diameter of Fountain:
?? ft.
3. Two circular flower beds of the same size will be included inside the garden. What is the diameter of
each flower bed? Select any whole number between 6–9 feet.
Diameter of Each Flower Bed:
?? ft.
4. A rectangular stone path will run from the fountain to the edge of the garden. What is the length and
width of the stone path? Select any whole number between 12–20 feet for the length and 2–5 feet for
the width.
Length of Path:
Width of Path:
?? ft.
?? ft.
Part Two: Answer questions 5–7. Show each step of your work. Some questions provide you with the
correct formula to use. If this is the case, replace the “?” in the formula template with the appropriate
values.
5. The pipe of a sprinkler system will run diagonally from one corner of the garden to the other corner.
What is the length of the pipe? Round to two decimal places if needed.
Hint: Use the Pythagorean Theorem, 𝑐 2 = 𝑎2 + 𝑏 2 , and solve for c. Let a = width and b = length of the
garden.
What is the length of the pipe? __________(rounded to two decimal places)
6. Grass will be laid in all areas of the garden that is not covered by the fountain, stone path, and flower
beds. How many square feet of grass will be needed to cover the remaining area? Follow the steps
listed below. Replace the “?” with the appropriate values in the formulas that follow.
Area for Grass = area of garden – area of stone path – area of fountain – area of both flower beds
a. Find the area of the garden:
𝐴 = 𝐿𝑒𝑛𝑔𝑡ℎ × 𝑊𝑖𝑑𝑡ℎ
𝐴 =?×?
𝐴 = ? 𝑓𝑡 2
b. Find the area of the stone path:
𝐴 = 𝐿𝑒𝑛𝑔𝑡ℎ × 𝑊𝑖𝑑𝑡ℎ
𝐴 =?×?
𝐴 = ? 𝑓𝑡 2
c.
Find the area of the fountain. Let 𝜋 = 3.14. Round to two decimal places. Note: Divide the
diameter by 2 to find the radius.
𝐴 = 𝜋𝑟 2
𝐴 = 3.14 × ?2
𝐴 = 3.14 × ?
𝐴 = ? 𝑓𝑡 2
d. Find the area of both flower beds. Let 𝜋 = 3.14. Round to two decimal places. Note: Divide the
diameter by 2 to find the radius.
To find the area of two flower beds of the same size, multiply the area formula by 2. This is
already reflected in the formula:
𝐴 = 2𝜋𝑟 2
𝐴 = 2 × 3.14 × ?2
𝐴 = 2 × 3.14 × ?
𝐴 =?×?
𝐴 = ? 𝑓𝑡 2
e. Substitute the values found in parts a – d into the formula below to find how much grass is
needed.
Area for Grass = area of garden – area of stone path – area of fountain – area of both flower beds
Area for grass = ? – ? – ? – ?
Area for grass = ? ft2
How many square feet of grass will be needed to cover the remaining area? _________
7. A border will be placed around each flower bed. How much material will be needed for both flower
beds? Round UP to the nearest foot (whole number).
Hint: Use the formula for circumference, 𝐶 = 2𝜋𝑟. Let 𝜋 = 3.14.
𝐶 = 2𝜋𝑟
𝐶 = 2 × 3.14 × 𝑟
𝐶 =?× 𝑟
𝐶 = ? 𝑓𝑡.
Multiply the value for circumference by 2 to find the total amount of material needed for both flower
beds:
2 × 𝑐𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = ? ?
How much material will be needed for both flower beds? _________(rounded UP to the nearest foot)