You may also like

Square Areas

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

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.

Tetra Square

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.

Dissect

Age 11 to 14 Challenge Level:

It is possible to dissect any square drawn on a grid into smaller squares, by cutting along grid lines.


For example a 3 by 3 square can be dissected into either 9 smaller squares or 6 squares:



  • What is the minimum number of squares a 13 by 13 square can be dissected into?
     
  • What is the smallest size square which can be dissected into squares which are all different sizes?