Quadrilaterals

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 parallelogram.

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 rhombus.

A farmer has a field which is the shape of a trapezium as illustrated below. To increase his profits he wishes to grow two different crops. To do this he would like to divide the field into two trapeziums each of equal area. How could he do this?

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

The points P, Q, R and S are the midpoints of the edges of a non-convex quadrilateral.What do you notice about the quadrilateral PQRS and its area?

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

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

Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.