These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

Draw three equal line segments in a unit circle to divide the circle into four parts of equal area.

Can you fill in the empty boxes in the grid with the right shape and colour?

Use the isometric grid paper to find the different polygons.

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Explain how the thirteen pieces making up the regular hexagon shown in the diagram can be re-assembled to form three smaller regular hexagons congruent to each other.

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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

Shogi tiles can form interesting shapes and patterns... I wonder whether they fit together to make a ring?

What shape and size of drinks mat is best for flipping and catching?

An environment that enables you to investigate tessellations of regular polygons

Two polygons fit together so that the exterior angle at each end of their shared side is 81 degrees. If both shapes now have to be regular could the angle still be 81 degrees?

Thinking of circles as polygons with an infinite number of sides - but how does this help us with our understanding of the circumference of circle as pi x d? This challenge investigates. . . .

This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.

Make five different quadrilaterals on a nine-point pegboard, without using the centre peg. Work out the angles in each quadrilateral you make. Now, what other relationships you can see?

Make an estimate of how many light fittings you can see. Was your estimate a good one? How can you decide?

What are the shortest distances between the centres of opposite faces of a regular solid dodecahedron on the surface and through the middle of the dodecahedron?

Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.

This LOGO challenge starts by looking at 10-sided polygons then generalises the findings to any polygon, putting particular emphasis on external angles

Given a 2 by 2 by 2 skeletal cube with one route `down' the cube. How many routes are there from A to B?

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.

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

Draw three straight lines to separate these shapes into four groups - each group must contain one of each shape.

This investigation explores using different shapes as the hands of the clock. What things occur as the the hands move.