Squares

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

Can you find the squares hidden on these coordinate grids?

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

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What sizes of rectangle contain exactly 100 squares? Can you find them all?

Can you recreate squares and rhombuses if you are only given a side or a diagonal?

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.

Four identical right angled triangles are drawn on the sides of a square. Two face out, two face in. Why do the four vertices marked with dots lie on one line?

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?