2D shapes and their properties

problem
Semicircle in a semicircle

Age

14 to 16

Challenge level

The diagram shows two semicircular arcs... What is the diameter of the shaded region?
problem
Hexapentagon

Age

11 to 14

Challenge level

Weekly Problem 53 - 2007
The diagram shows a regular pentagon and regular hexagon which overlap. What is the value of x?
problem
Like a circle in a spiral

Age

7 to 16

Challenge level

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?
problem
Spirostars

Age

16 to 18

Challenge level

A spiropath is a sequence of connected line segments end to end taking different directions. The same spiropath is iterated. When does it cycle and when does it go on indefinitely?
problem
2 rings

Age

5 to 7

Challenge level

The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?
problem
Triangular hexagons

Age

7 to 11

Challenge level

Investigate these hexagons drawn from different sized equilateral triangles.
problem
LOGO challenge 12 - concentric circles

Age

11 to 16

Challenge level

Can you reproduce the design comprising a series of concentric circles? Test your understanding of the realtionship betwwn the circumference and diameter of a circle.
problem
LOGO challenge 11 - more on circles

Age

11 to 16

Challenge level

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 relationship.
problem
Torn shapes

Age

7 to 11

Challenge level

These rectangles have been torn. How many squares did each one have inside it before it was ripped?
problem
Trapezium four

Age

14 to 16

Challenge level

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