2D shapes and their properties

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

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

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?

How efficiently can you pack together disks?

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

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

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

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.

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

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?