## Area of regular polygons

This resource came from a team challenge question at SEAMC 2015 (South East Asia Mathematics Competition). I gave it to my top set year 10s as a starter and it had so much scope that it turned into a whole lesson! It looks at area, pythagoras, surds, algebra and maybe some trigonometry.

Pupils start off with the question, how to find the area of a regular hexagon with sides of 4cm. This comes with an optional hint of: divide into equilateral triangles. The problem alongside this is find the area of a regular octagon with sides of 4cm. This is a bit trickier and can be used to differentiate the lesson early on. The area of a regular octagon can be found by drawing a square around the outside.

Once pupils have worked out the areas, ask them to generalise a formula for an n-sided hexagon and octagon. This can be helped by working through the solution to the four sided shape step by step and asking for pupils to replace 4 with n.

I have included a "help" sheet to try and support students who are struggling. One student of mine managed to generalise a formula for any regular polygon, using the internal angles of a polygon and trigonometry to split shapes into right angled triangles. I created some videos on Youtube to work through solutions. It might be nice to ask students to create their own videos or posters explaining how to find the areas of regular polygons.

Pupils start off with the question, how to find the area of a regular hexagon with sides of 4cm. This comes with an optional hint of: divide into equilateral triangles. The problem alongside this is find the area of a regular octagon with sides of 4cm. This is a bit trickier and can be used to differentiate the lesson early on. The area of a regular octagon can be found by drawing a square around the outside.

Once pupils have worked out the areas, ask them to generalise a formula for an n-sided hexagon and octagon. This can be helped by working through the solution to the four sided shape step by step and asking for pupils to replace 4 with n.

I have included a "help" sheet to try and support students who are struggling. One student of mine managed to generalise a formula for any regular polygon, using the internal angles of a polygon and trigonometry to split shapes into right angled triangles. I created some videos on Youtube to work through solutions. It might be nice to ask students to create their own videos or posters explaining how to find the areas of regular polygons.

investigating_the_area_of_polygons.pptx | |

File Size: | 394 kb |

File Type: | pptx |

investigating_the_area_of_polygons_ws.docx | |

File Size: | 42 kb |

File Type: | docx |