Math Problem Statement

A property survey is a professional assessment of a property’s boundaries, size, location, and features like a house. On this page you will draw a property survey with a house on it. You will use this property survey to answer questions on the next page. Draw a sketch of a property survey with a house on it that you might one day own (or of the one you already do own or live in). This is an aerial view so you don’t need to have any artistic skills. You can be as simple of complex with your drawing as you want. Things will be easier if you only draw lines to create each requested item. Hold onto this drawing, you will use it on the next test where we do some personal finance work with it. 5. Start by drawing the outline of the property and include all the measurements in feet. Inside the property lot draw an outline of a house and include all measurements in feet. (2) 6. Let’s imagine that the backyard is not at all done. Using a dotted line, draw in where you would put a fence in order to show where your backyard is. (2) Include all the measurements of the fence in feet. 7. Lightly shade in or color in the backyard. (2) 8. Looking at the shading or coloring that creates the backyard notice along the perimeter there are angles. Label each angle of the backyard in the picture as either acute, obtuse, or right. (2) 9. Choose one corner that has a right angle along the fence to be a triangular fire pit corner. Decide how long you want the edges along the fence to be and mark that measurement in feet on your drawing. Connect those to make the triangle and color in that space darker or with a different color. (2)

  1. Fence is sold by the foot. Based on the picture you just created find out how many feet of fence you would need to purchase. a) Understand the situation (2) b) Make a plan (4) c) Execute the plan (4) d) Reflect on your answer (2)
  2. If you’re going to use a single line of pavers to create the fire pit corner, how many feet of pavers will you need? (4) Hint: Use Pythagorean Theorem to find the missing edge of the triangle that is in the grass.
  3. Based on the picture you just created find out how many square feet of grass you will need to order/purchase to cover the backyard in grass. a) Understand the situation (2) b) Make a plan (4) c) Execute the plan (4) d) Reflect on your answer (2)
  4. A pallet of grass covers 500 square feet. Alternatively, a single sod piece covers approximately 2.66 square feet. How many pallets would you need to buy if you decided to buy pallets? (4) How many single sod pieces would you need to buy if you decided to buy single sod pieces? (4)

Solution

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Math Problem Analysis

Mathematical Concepts

Geometry
Trigonometry
Area Calculation
Perimeter Calculation
Pythagorean Theorem

Formulas

Area of a rectangle: A = length × width
Perimeter of a rectangle: P = 2 × (length + width)
Pythagorean Theorem: c^2 = a^2 + b^2

Theorems

Pythagorean Theorem

Suitable Grade Level

Grades 8-10