2D shapes and their properties

problem
Bicentric quadrilaterals

Age

14 to 16

Challenge level

Investigate the properties of quadrilaterals which can be drawn with a circle just touching each side and another circle just touching each vertex.
problem
Curvy areas

Age

14 to 16

Challenge level

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?
problem
Diagonal division

Age

11 to 14

Challenge level

Weekly Problem 45 - 2008
The diagram shows a regular pentagon with two of its diagonals. If all the diagonals are drawn in, into how many areas will the pentagon be divided?
problem
Efficient packing

Age

14 to 16

Challenge level

How efficiently can you pack together disks?
problem
Logic block collections

Age

5 to 7

Challenge level

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?
problem
Shapes in the alphabet

Age

5 to 7

Challenge level

In this problem, we're going to find sets of letter shapes that go together.
problem
Shaping up

Age

7 to 11

Challenge level

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?
problem
Overlapping again

Age

7 to 11

Challenge level

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.
problem
Angle to chord

Age

14 to 16

Challenge level

Weekly Problem 23 - 2008
A triangle has been drawn inside this circle. Can you find the length of the chord it forms?
problem
Oh so circular

Age

14 to 16

Challenge level

The diagram shows two circles and four equal semi-circular arcs. The area of the inner shaded circle is 1. What is the area of the outer circle?