Six circular discs, all of radius 1 unit, are packed in different-shaped boxes so that the discs touch their neighbours and the sides of the box.

- Without using any calculations, compare the areas of the bases of boxes A and B and say which is the larger.
- Use estimation to list the packings in order of increasing base area. Which are the hardest to put in order?
- Now calculate the area of the base of each box and compare the correct order with your estimate.

Sine, cosine, tangent. Regular polygons and circles. Pythagoras' theorem. Cartesian equations of circles. Trigonometric identities. Sine rule & cosine rule. 2D shapes and their properties. Mathematical reasoning & proof. Circle properties and circle theorems. Area - triangles, quadrilaterals, compound shapes.