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Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

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Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

Shear Magic

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2
Lots of you wrote in to say that the areas of all the different triangles in the family was 1 square unit.

Luke of All Saints School gave the following explanation:

any 'family' of triangle with an equal bases and heights will have the same area because the area of a triangle is (base x height)/2.

when the base and height are always the same then the areas of the different triangles are always the same.

here the triangles have 1 unit in the base and 2 units in the height their area will always be 1 sq. unit.