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Great Squares

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

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Paving the Way

A man paved a square courtyard and then decided that it was too small. He took up the tiles, bought 100 more and used them to pave another square courtyard. How many tiles did he use altogether?

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Chess

What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?

Square Areas

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The outer square has sides of length 1.

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