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Shear Magic

Age 11 to 14 Challenge Level:

All these triangles have a base of 1 unit and a height of 2 units. We could call them a "family" of triangles.

1 by 2 right angled triangle sheared 1 by 2 right angled triangle more sheared 1 by 2 right angled triangle very sheared 1 by 2 right angled triangle

What are their areas? What do you notice?

Can you generalise to other "families" of triangles?