Squares

problem
Ten hidden squares

Age

7 to 14

Challenge level

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
problem
Something in common

Age

14 to 16

Challenge level

A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.
problem
Square it

Age

11 to 16

Challenge level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
problem
On the edge

Age

11 to 14

Challenge level

If you move the tiles around, can you make squares with different coloured edges?
problem
Tilted squares

Age

11 to 14

Challenge level

It's easy to work out the areas of most squares that we meet, but what if they were tilted?
problem
Circle box

Age

14 to 16

Challenge level

It is obvious that we can fit four circles of diameter 1 unit in a square of side 2 without overlapping. What is the smallest square into which we can fit 3 circles of diameter 1 unit?
problem
A square in a circle

Age

7 to 11

Challenge level

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?
problem
Inside seven squares

Age

7 to 11

Challenge level

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?
problem
Squares, squares and more squares

Age

11 to 14

Challenge level

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?
problem
Two triangles in a square

Age

14 to 16

Challenge level

Given that ABCD is a square, M is the mid point of AD and CP is perpendicular to MB with P on MB, prove DP = DC.