Quadrilaterals

problem
Rectangle tangle

Age

7 to 11

Challenge level

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the shapes?
problem
Numerically equal

Age

7 to 11

Challenge level

Can you draw a square in which the perimeter is numerically equal to the area?
problem
Quadrilaterals

Age

7 to 11

Challenge level

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?
problem
Cyclic quad jigsaw

Age

14 to 16

Challenge level

A picture is made by joining five small quadrilaterals together to make a large quadrilateral. Is it possible to draw a similar picture if all the small quadrilaterals are cyclic?
problem
Linkage

Age

11 to 14

Challenge level

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?
problem
Arrowhead

Age

14 to 16

Challenge level

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?
problem
Quad in quad

Age

14 to 18

Challenge level

Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?
problem
Hexagon transformations

Age

7 to 11

Challenge level

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!
problem
Dividing the field

Age

14 to 16

Challenge level

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?
problem
Flexi quads

Age

16 to 18

Challenge level

A quadrilateral changes shape with the edge lengths constant. Show the scalar product of the diagonals is constant. If the diagonals are perpendicular in one position are they always perpendicular?