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.

Attachments

AreaOfPentagon_full.pdf583.24 KB

AreaOfPentagon_arithmetic.pdf189.85 KB