Quadrilaterals

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
Favourite

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
Favourite

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
Favourite

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
Favourite

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?
problem

Cut and Make

Age

7 to 11

Challenge level

Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?
problem

Is a Square a Rectangle?

Age

7 to 11

Challenge level

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?