Quadrilaterals

problem
Unusual quadrilateral

Age

14 to 16

Challenge level

This quadrilateral has an unusual shape. Are you able to find its area?
problem
Biggest bendy

Age

16 to 18

Challenge level

Four rods are hinged at their ends to form a quadrilateral. How can you maximise its area?
problem
Strange rectangle

Age

16 to 18

Challenge level

ABCD is a rectangle and P, Q, R and S are moveable points on the edges dividing the edges in certain ratios. Strangely PQRS is always a cyclic quadrilateral and you can find the angles.
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
Tangram tangle

Age

5 to 7

Challenge level

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
problem
Cutting it out

Age

5 to 11

Challenge level

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

Age

5 to 11

Challenge level

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.
problem
Poly plug rectangles

Age

5 to 11

Challenge level

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?
problem
Folding flowers 1

Age

7 to 11

Challenge level

Can you visualise what shape this piece of paper will make when it is folded?
problem
Bracelets

Age

7 to 11

Challenge level

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?