Recommending the Purchase of a Plot of Land
Name: Date:
Recommending the Purchase of a Plot of Land
Geometry Chapter 9 Portfolio Project
OBJECTIVE: Find and compare the costs of two pieces of property.
Goals: • Follow a directional pattern.
• Create and use a scale drawing.
• Use the Pythagorean Theorem and special right triangles.
• Determine the total area of irregularly shaped property.
MATERIALS: graph paper, ruler, calculator, and computer (optional)
INVESTIGATION: Your parents want your help in analyzing two plots of land they are considering purchasing. Your parents have measured the size of each property by walking in a pattern, making right and left turns of 90°. The boundaries of the property are the lines connecting the stakes. You have the following descriptions:
Lot 1: Begin at stake 1, go right 180 ft to stake 2, turn right, go 120 ft, turn right and go 60 ft to stake 3, go straight 60 ft, turn left, go 60 ft, turn left and go 60 ft to stake 4, turn right, go 60 ft, turn right and go
60 ft to stake 5, go straight 120 ft, turn right and go 90 ft to stake 6, turn left, go 30 ft, turn right and go 90 ft to stake 7, turn right, go 90 ft, turn left and go 60 ft, returning to stake 1.
Lot 2: Begin at stake 1, go right 100 ft to stake 2, turn right, go 50 ft, turn right and go 25 ft to stake 3, turn left, go 25 ft, turn left and go 75 ft to stake 4, turn right, go 100 ft, turn right and go 100 ft to stake 5,
go straight 75 ft to stake 6, turn right, go 75 ft, turn left and go 50 ft to stake 7, turn right go 100 ft, turn right and go 75 ft, returning to stake 1.
1. Draw a diagram for each piece of property showing your parents’ path. Identify the scale you are using and mark the location of each stake.
2. Draw another diagram showing the actual outline of each piece of property. Use the same scale and mark the location of each stake.
3. Find the perimeter and area of each piece of property. Explain your methods and show your calculations.
4. Determine the cost of fencing the properties. Fencing costs $6.75 per foot.
5. Determine the cost of the taxes for the first year. Taxes for Lot 1 are $683.54 per acre. Lot 2 is in another town where taxes are $725.38 per acre. (Hint: There are 43,560 square feet in one acre.)
6. Based on the cost of the taxes and fencing, describe any advantages of purchasing each piece of property.
7. Which piece of property would you recommend that your parents purchase if Lot 1 is selling for $12,500 and Lot 2 is selling for $11,800? Explain.
Present your results in a report that contains all of the diagrams. You should explain your methods and show your calculations for determining the area, perimeter, fencing costs, and taxes. Include an examination of any right triangles you formed in calculating area or perimeter. Are any of them similar? Are there any special right triangles? If so, explain how you can use those relationships in finding or checking measurements. Discuss the advantages and disadvantages of each property. Make and support a recommendation to your parents about which piece of property to purchase. Include your reflection. If you work with another student, you must each turn in your own discussion of advantages and disadvantages, your recommendation, and your reflection.