Pythagoras' theorem with other polygons

Last updated: 15/11/2023
Contributor: David Benjamin 🐝
Pythagoras' theorem with other polygons
Main Subject
Key stage
Category
Geometry and measures: Pythagoras' theorem
Inside
Includes answers
Resource type
Student activity
Maths
Reasoning

Does Pythagoras' theorem work with shapes that are not squares? If the squares on the sides of a right-angled triangle are replaced by other regular polygons, does the sum of the areas of the two smaller polygons equal the area of the largest polygon?

This investigation can provide great practice on using the sine rule for the area of a triangle, although can also be done without, and calculating the area of any regular polygon.

If students attempt the extension and find the formula for regular n-gons on the sides of a right-angled triangle, they will use some lovely trigonometry in their derivation and proof.

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