Six circles, all of radius 1 unit, are packed in 4 different shaped boxes so that the circles touch their neighbours and the sides of the box.

  1. Without using any calculations, compare the areas of the boxes (A) and (B) and say which is the larger.
  2. By guesswork, list the four packings in order of increasing area of the boxes.
  3. Calculate the area of each box. Was your guess correct?
6 circles in a triangle. 6 circles in a parallelogram.
6 circles in a long rectangle. 6 circles in a rectangle.