do not enclose any crossing grid lines and Perimeter and area N4.1 Core Starter Investigate any connection between the area and perimeter of shapes which do not enclose any crossing grid lines and whose sides meet at right angles at all vertices. Does your rule hold (is it valid) for shapes with a hole in? Preamble This activity gives pupils the opportunity to carry out an investigation given some conditions and to work systematically to try to find a rule. The result is based on Pick’s theorem: area = inside points + (points on the perimeter ÷ 2) – 1 Some pupils may need reminding of the conditions – all vertices right angles and no grid lines crossing inside the shape. Possible content Working out areas and perimeters of rectilinear shapes, recording results in a systematic way, generalising. Resources Centimetre-squared paper. Solution/Notes Given the stated conditions, the rule is: area = perimeter ÷ 2 − 1 This holds for ‘U’ shapes, but for shapes with a hole in it becomes: area = perimeter ÷ 2 An extension investigation would be to consider the case of two holes etc. Original Material © Cambridge University Press 2009 Original Material © Cambridge University Press 2009