Quadrilaterals

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

I cut this square into two different shapes. What can you say about the relationship between them?

What does the overlap of these two shapes look like? Try picturing it in your head and then use some cut-out shapes to test your prediction.

Weekly Problem 8 - 2008
In how many ways can a square be cut in half using a single straight line cut?

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

Can you find the area of a parallelogram defined by two vectors?

A game in which players take it in turns to try to draw quadrilaterals (or triangles) with particular properties. Is it possible to fill the game grid?

A game in which players take it in turns to turn up two cards. If they can draw a triangle which satisfies both properties they win the pair of cards. And a few challenging questions to follow...

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!