Squares

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.

ABCD is a square. P is the midpoint of AB and is joined to C. A line from D perpendicular to PC meets the line at the point Q. Prove AQ = AD.

Cut off three right angled isosceles triangles to produce a pentagon. With two lines, cut the pentagon into three parts which can be rearranged into another square.

If you continue the pattern, can you predict what each of the following areas will be? Try to explain your prediction.

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.

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?

Why do you think that the red player chose that particular dot in this game of Seeing Squares?

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