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Area of a Triangle - Lesson Plans

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					Calculating in Construction – Area of a Triangle




                                   Area of a Triangle
Lesson Focus
This lesson is to help learners understand the concepts involved in calculating the
area of a triangle.

Knowledge of the following numeracy skills:
       Ability to use a calculator for basic operations (multiplication)
       An understanding of the metric units for length mm and m
       An understanding of calculating a basic rectangular area

How this maths skill can be reinforced on the job:
Triangles are often used in construction, such as in roofing and in the construction of
frames, as their shape provides stability. This skill can be reinforced when
completing triangular shaped jobs such as:

 In Civil Construction, when coating or sealing a triangular shaped surface, when
  performing concrete repairs and painting or anti-graffiti treatment, when
  conducting grader or scraper or roller operations, when spraying tack coat, when
  rolling aggregate, when conducting pavement sweeping operations, when
  conducting road maintenance operations, when compacting asphalt, when
  spreading and compacting landfill and when conducting paver operations.

 In Offsite Construction, determining the area of a triangular shaped excavation
  site, when coating surfaces, in the construction of frames and windows, or in
  roofing.

 In General Construction, when preparing and laying triangular shaped concrete
  slabs, when repairing and renovating areas of roof tiles, when fixing plasterboard
  wall and ceiling sheets, when fixing or repairing wall tiles, when preparing surfaces
  for waterproofing or when constructing a section of brick veneer building or brick
  walls.

   In Painting and Plastering, when preparing or coating surfaces, when estimating
    material quantities such as wall paper, paint stripper stains, finishes, paint and
    when preparing wall and ceiling surfaces.

 In Furnishing, when preparing and laying underlay for flooring, when patching and
  repairing floors, when preparing surfaces for finishing , when glazing windows and
  doors and when costing materials for various shaped furniture.

 In Plumbing, when estimating quantities and costs for a job, or when calculating
  the size and area of triangular shaped site or job to be done, when excavating, in
  roofing, in the construction of frames, when calculating gable ends on buildings.

Lesson time:
       Approximately 20 minutes

Materials needed for this lesson:
       Two worksheets for each learner
       Calculator for each learner
       Whiteboard

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Calculating in Construction – Area of a Triangle




Lesson breakdown:

The suggested lesson plan should be delivered as follows:



        Step               Trainer / Learner Activity


           1               Introduction of the area of a triangle formula


           2               Worked example 1 of area of a triangle


           3               Worked example 2 of area of a triangle


           4               Learners complete the area of a triangle worksheets 1 and 2 with
                           trainer support and answers




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Calculating in Construction – Area of a Triangle




1.      Introduction or explanation of the formula for the area of a triangle.




       Remind learners the area of a rectangle is given by the formula
                                   A  L  W (Area = length x width)


Example

The area of this rectangle:                                             8m
           A  8 5
              40 m 2

                                                                                5m




     The area of a triangle is half the area of the rectangle with the same base length
      and height (rectangle width)

Example

The area of each triangle shown is:                                     8m
                1
           A     85
                2
               20 m 2                                                          5m




    The formula for calculating triangle area is:
                                                      1
                                             Area       base  height
                                                      2
      or in symbols:
                                                   1
                                              A     bh
                                                   2




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Calculating in Construction – Area of a Triangle




2. Example 1



Find the area of the triangle below




                                3.2 m




                                                   4.5 m

              1
        A       4.5  3.2
              2
             7.2 m 2


        Note: with a calculator we type 0.5 x 4.5 x 3.2 =




3. Example 2


Find the area of this triangle.


                                                                                3.6 m




                                                           8m
                     1
                A      8  3.6
                     2
                    14 .4 m 2




4.      Learners complete the worksheets with trainer assistance or
        answers available.




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Calculating in Construction – Area of a Triangle




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Calculating in Construction – Area of a Triangle




      Area of a Triangle Worksheet Answers




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Calculating in Construction – Area of a Triangle




                 Area of a Triangle Worksheet 2
1. Which has the larger area, the triangle or the shaded area and by how much is it
   bigger?



                                          55 mm




                    46 mm




2.    The scoop on this front end loader is made up of 2 triangles and 2 rectangles
      welded together.
      What is the area of metal needed to make the scoop?




3.      Calculate the area of the site shown below.
                                               6m


                                                                        5m

                                                                                18 m

              4m

                     .
                          5m

                                             26 m                                .




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Calculating in Construction – Area of a Triangle




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