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Unit IV Assignment: Backyard Shapes

In this assignment, you will be asked to find specific information related to the area and perimeter of a backyard you are designing.

Instructions: Imagine that you are landscaper who is designing a backyard for your clients. The backyard must contain a pond, flower bed with a sprinkler system, a pool with a concrete border, and a patio with an awning. These features can be placed anywhere inside the backyard. An example of a design is shown below. Answer questions 1–8. Save all your work to this template and submit it in Blackboard for grading.

Part One: For questions 1–4, identify the dimensions of the components in the backyard. 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. A square flower bed will be included inside the garden. What is the length of each side of the flower bed? Select any whole number between 10–15 feet.

1. A rectangular pool will be included in the backyard. What is the length and width of the pool? Select any whole number between 30 – 36 for the length and 15 – 18 feet for the width.

1. A rectangular patio will be included in the backyard. What is the length and width of the patio? Select any whole number between 20 – 30 feet for the length and 15 – 20 feet for the width.

1. A circular pond will be included inside the backyard. What is the circumference of the pond? Select any whole number between 16–25 feet.

Part Two: Use the information you provided in Part One to answer questions 5–8. 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.

1. The pipe of a sprinkler system will run diagonally from one corner of the flower bed to the other corner. What is the length of the pipe? Round to two decimal places if needed. You must show your step-by-step work.

Hint: Use the Pythagorean theorem, a2 + b2 = c2 and solve for c. Let a = width and b = length of the of the flower bed. The value for the length of each side of the square flower bed was identified in problem 1 above.

Notes for showing your work: You can use the ^ key on your keyboard to represent exponents. For example, you can write a2 as a^2. You can also use the letters SQRT to represent the square root.

For example, you can write as SQRT(4).

What is the length of the pipe? __________ (rounded to two decimal places)

1. An 8-foot border of concrete will be included around the pool. How much concrete will be needed? Use the diagram below to complete Parts a–d. The dimensions of the pool were identified in problem 2 above.

Area of Concrete = Area of large rectangle – Area of pool

1. Find the area of the larger rectangle. Use the diagram above to help you determine the length and width of the rectangle. Replace the “?” with the appropriate values in the formula that follows.

A = length x width

A = ? x ?

A = ? ft2

1. Find the area of the pool. Replace the “?” with the appropriate values in the formula that follows.

A = length x width

A = ? x ?

A = ? ft2

1. Substitute the values found in parts a and b into the formula below to find how much concrete is needed.

Area of Concrete = Area of large rectangle – Area of pool

Area of Concrete = ? – ?

Area of Concrete = ? ft2

What is the area of the concrete border around the pool? ________

1. Concrete is sold by the cubic yard, and one cubic yard of concrete will cover 81 square feet when it is 4 inches deep.

Determine the amount of concrete needed for the concrete border around the pool by dividing the answer obtained in part c by 81. This value will represent the cubic yards of concrete needed for the job. Show work below.

How much concrete is needed for the job? _________

1. An awning will be placed above the patio. The awning will be in the shape of a trapezoid. The height, h, of the trapezoid is half the width of the patio. B1 is the length of the patio. B2 is 4 feet shorter than the length of the patio. How much fabric is needed for the awning? If your answer is a decimal value, round to two decimal places. Replace the “?” with the appropriate values in the formula that follows.

A = ½ h(b1 + b2)

A = ½ (?)(? + ?)

A = ½ (?)(?)

A = ½ (?)

A = ? ft2

How much square feet of fabric is needed? __________

1. The circular pond will have a curved bench around a part of the edge. Use the proportion below to determine the length of curved bench. Assume that the measure of central angle ACB is 100 degrees. The value for the circumference of the pond was identified in problem 4 above.

Substitute the values for the measure of angle ACB and the circumference into the following proportion and solve. Let X be the length of arc AB. Use the template below to get started. Make sure to show all steps of your work.

measure of angle ACB = length of arc AB

360o circumference of circle

? = _X______

360o ?

Use the space below to continue solving the proportion.

What is the length of the curved bench? __________