Constructing a Shed

CLA - SHSM - MCR3U, Gr. 11 Univ. Math, Fletcher's Meadow SS

Your Task

You have been asked to come up with a plan to build a shed for your math teacher. Refer to the diagrams below to

  • calculate necessary areas of the shed
  • determine the amount of material required
  • prepare a written estimate

Your teacher has to borrow the money to pay you, so you will


  • determine the cost of borrowing and
  • research a career in construction and make a flyer
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Round off your answers to one decimal place where necessary.

1. To calculate the total roof area.

a) In diagram 3, if BD = AD, calculate the length BC. You may watch this video to help you answer this question. [2 marks]
1 1 SohCahToa with sides

2. To calculate the total wall area.

a) Find CD and calculate the total shed height taking help of the video link provided here.

[2 marks]https://www.youtube.com/watch?v=f7e46PdG4iA

b) Calculate the area of the door and the window. The dimensions for the window are listed in diagram 1 and dimensions for the door are listed in diagram 2.[2 marks]




c) Now calculate the total area of all walls. Assume that there is just one door and one window in the shed. Make sure to subtract the area of a window and area of the door.[4 marks]

3. To determine material needed to complete the job.

a) Use the total area to determine the number of sheets of plywood needed to build the shed, i.e. sides and a roof. Include 10% plywood to account for cutting waste. Each sheet of plywood is 1.2 m by 2.4 m. Watch the following video to help you calculate % of a whole number. [4 marks]
How to work out percentages of whole numbers
b) Use the total roof area to determine the number of bundles of shingles required to shingle the roof. Each bundle of shingles covers approximately 2.8 square meters. Add an extra 10% to account for waste and overlap. [ 4 marks]

4. Prepare a written estimate for the job.

Using internet, find the cost of some of the items at local hardware or building stores, e.g Home Depot, Rona etc. Make sure you get 1 quote.


Given: You will use pre-made trusses to build the roof and they are shown in the top half of Diagram 2. The total cost of the 2 trusses (front & back), along with the framing studes, is approximately $1100 delivered, plus HST. The screws and nails needed for the job will cost $50, plus HST.


a) Determine the cost of the plywood needed to build walls and roof of the shed. Online, you may want to find the cost of a plywood sheet that is 4 foot by 8 foot; choose the appropriate thickness of the plywood sheet for the job. The plywood sheet of 4 foot by 8 foot is approximately the same size and cost, as a 1.2 m by 2.4 m sheet of plywood. [ 2 marks]


b) Determine the cost of the shingles needed. [2 marks]


c) To estimate the labour costs: [3 marks]


There is a concrete slab base that has been poured for the floor of the shed so you don't need to include that expense in your estimate.


Do some research and include the following in your estimate:


- your hourly rate that you will charge: ___________

- number of hours to complete the job: ____________

- total labour charges:


d) Determine the total estimated cost of the shed including labour and materials. Your supplier has the window you need on sale for $110, and the door is $200. Remember that materials and labour have HST costs. [6 marks]

5. Borrowing to pay for the project.

Your teacher doesn't have the money to pay for the project at this time, but he/she do need to have the shed. so, your teacher borrows money from the line of credit.


Your teacher has two payment options.


Option A:

The money can be borrowed at 5.8% compounded monthly. Calculate the amount that your teacher will have to pay in 3 years when the project is paid for. [2 marks]


Option B:

Your teacher can put down $500 and borrow the rest at 6.5% compounded semi-annually. Calculate the total cost your teacher will have to pay using this option if the balance of the cost is paid off in 3 years. [2 marks]


You may watch the following video to understand how to calculate amount.

8.2 Compound Interest (Future Value)
b) Which is the better option for your teacher and how much money will be saved? Explain. [2 marks]

6. Make a flyer

Pick a career in construction, to research, that may use these skills. Include the following information.


  • Job description
  • Education/Experience required
  • Working conditions
  • Typical salary upon graduation
  • # of working hours/week
  • Perks of choosing this career
  • Mathematical knowledge required


Refer to the following rubric.

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