Square Areas

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

Dissect

What is the minimum number of squares a 13 by 13 square can be dissected into?

2001 Spatial Oddity

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

Squares in Rectangles

Age 11 to 14 Challenge Level:

A $2$ by $3$ rectangle contains $8$ squares. Can you see how?

A $3$ by $4$ rectangle contains $20$ squares. Can you see how?

A $4$ by $6$ rectangle contains $50$ squares. Can you see how?

What size rectangle contains exactly $100$ squares?

Is there more than one?
Can you find them all?
Can you prove that there are no more?

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