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Area of Composite Shapes

Shapes in the real world come in all sizes. Learn how to break down and calculate the area of composite shapes using the sum of areas of each part.

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Puzzling Triangles

Ancient Chinese philosophers used models of shapes to study geometry. Over time, other people in China began to use the shapes to make puzzles, called tangrams. When a sea captain introduced tangrams to the rest of the world, they quickly became a popular game.


The seven shapes in a standard tangram are all 45-45-90 triangles or shapes made by combining 45-45-90 triangles—namely, a square and parallelogram. You can arrange the pieces into various composite shapes that together can resemble boats, birds, people, and other designs.

Credit: Mark Turnauckas
Source: http://www.flickr.com/photos/marktee/6086755084/
License: CC BY-NC 3.0

The first book of tangrams contained around 300 shape puzzles. However, the seven pieces can make billions of shapes.

One reason tangrams remain popular is that people do not need to share a language to enjoy tangrams. The puzzles can challenge and delight both children and adults, as well as people from many different cultures. You can make your own tangram set out of paper. All you need is a printer and a pair of scissors, and you can start creating your own designs and puzzles with 45-45-90 triangles.

See for yourself: http://www.auntannie.com/Geometric/Tangrams/

Explore More

Hooked on tangrams? Below are more puzzles for you to try.




Image Attributions

  1. [1]^ Credit: Mark Turnauckas; Source: http://www.flickr.com/photos/marktee/6086755084/; License: CC BY-NC 3.0

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