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Learning objects Area of triangles: height intersects with the base outside the triangle


Find the area of triangles with vertical or horizontal sides. In this type of triangle, the base may be chosen so that the height intersects with the base outside the triangle. Explore how the formula for finding the area of a triangle works. First, estimate the area of a chosen triangle on a grid. Next, work out the correct formula by assembling a series of triangles and rectangles. Then, compare the actual area of the triangle with your original estimate. Practise applying the formula directly to a range of triangles. This learning object is one in a series of four objects.

Educational details

Key learning objectives
  • Students estimate the area of triangles.
  • Students identify the base and height pairs of triangles, including those situations where the height intersects the base outside the triangle.
  • Students identify the relationship between area of triangles and rectangles.
  • Students establish that all three base-height pairs can be used to calculate the area of triangles.
  • Students identify and apply the correct formula for calculating the area of a triangle.
Educational value
  • Provides a randomised range of triangle shapes on a square grid to help students estimate triangle areas.
  • Provides students with the choice of nominating the base and height pair of each triangle.
  • Demonstrates the link between the area of a triangle and the surrounding rectangle formed on the triangle base via manipulation strategies, visual representations and equation forms.
  • Provides written clues and prompts to aid student progress as they practise finding the area of triangles using base and height lengths found on the grid.
  • Alerts students to the accuracy of their estimation.
Year level

7; 8

Learning area
  • mathematics
  • Mathematics/Measurement and geometry
    • Mathematics/Triangles
    • Mathematics/Area
    • Mathematics/Formulas
    • Analysis;
    • Application;
    • Comprehension;
    • Knowledge
    Student activity
    • Interactives;
    • Analysis;
    • Problem solving;
    • Modelling
    Learning design
    • Independent learning;
    • Experiential learning;
    • Problem solving;
    • Visual learning

    Other details

    • Subject matter expert
    • Organisation: University of Western Sydney
    • Address: Penrith South NSW 2750 Australia
    • URL:
    • Technical implementer
    • Publisher
    • Date of contribution: 20 Sep 2013
    • Organisation: Education Services Australia
    • Address: Melbourne VIC 3000 Australia
    • URL:
    Access profile
    • Colour independence
    • Hearing independence
    Learning resource type
    • Interactive Resource
    • Microsoft Internet Explorer - minimum version: 8.0 (MS-Windows) - maximum version: 9.0 (MS-Windows)
    • Firefox - minimum version: (MS-Windows)
    • Safari - minimum version: 5.1 (MacOS)
    Operating systems
    • MacOS - minimum version: 10.6
    • MS-Windows - minimum version: XP - maximum version: 7
    • © Education Services Australia Ltd, 2013, except where indicated under Acknowledgements.