Area of a regular pentagon

Purpose

The purpose of this multi-level task is to engage students in a task that requires them to apply geometric properties of polygons and right angles triangle techniques in solving for the area of a polygon.

Description of Mathematics

The background knowledge presumed for this task is outlined in the diagram below:

The task can be presented with graded expectations to provide appropriate challenge for individual learning needs.

Activity

 

Task: By breaking down into triangles and/or rectangles, find the area of a regular pentagon of side length 10 cm.

 

 

The arithmetic approach (show more)

  • The student is able to apply geometric properties of polygons and to use trigonometric ratios to find an unknown area.

The procedural algebraic approach (show more)

  • The student is able to divide a regular polygon into composite triangles and rectangles and apply geometric properties of polygons and to use trigonometric ratios and Pythagoras' theorem to find an unknown area.

The conceptual algebraic approach (show more)

  • The student is able to divide a regular polygon into composite triangles and rectangles and apply geometric properties of polygons and to use trigonometric ratios and Pythagoras' theorem to find an unknown area.

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