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The Guides for Effective Instruction in Mathematics Revised

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E2.6 Show that two-dimensional shapes with the same area can have different perimeters, and solve related problems.

Activity 1: Generalization Activity for Area - Shapes with the Same Area

Goal

This activity helps students consolidate their understanding of measuring the area of a surface.

Note: Two shapes with equal areas are not always congruent.

Material

Instructions

Using a geoboard, a grid or a ruler, construct each of the shapes in your notebook.

Two rectangles of different dimensions with an area of 8 square units.

A rectangle and a parallelogram whose area is 12 square units.

A rectangle and a square whose area is 16 square units.

A rectangle and a triangle whose area is 6 square units.

A parallelogram and a triangle whose area is 10 square units.

A trapezoid and a parallelogram whose area is 12 square units.

A rectangle and a trapezoid whose area is 12 square units.

Source: translated from L'@telier - Ressources pédagogiques en ligne (atelier.on.ca).

Activity 2: Generalization Activity for Area - Areas of Shapes with the Same Perimeter

Goal

This activity helps students distinguish between the area and perimeter of a shape.

Material

  • geoboard
  • Appendix 5 (geoboard paper)
  • Appendix 4 (1 cm x 1 cm grid 
  • ruler graduated in centimetres

Instructions

Using a geoplan, grid or ruler:

    1. Construct a rectangle and a square with a perimeter of 24 units. (Note: Sides cannot be diagonal lines.)
    2. Determine the area of each of the quadrilaterals.
    3. Reproduce these shapes in your notebook.
    1. Construct two quadrilaterals with a perimeter of 20 units. (Note: Sides cannot be diagonal lines.)
    2. Determine the area of each of the quadrilaterals.
    3. Reproduce these quadrilaterals in the notebook.
    1. Construct three polygons with a perimeter of 32 units. (Note: Sides cannot be diagonal lines.)
    2. Determine the area of each of the polygons.
    3. Reproduce these polygons in the notebook.

Source: translated from L'@telier - Ressources pédagogiques en ligne (atelier.on.ca).