Elaboration on this Achievement Objective
Students should create formulae for perimeters and areas of polygons by attending to features of those polygons. For perimeters they should recognise when side lengths are equal and use multiplicative strategies rather than additive ones. For example to calculate the perimeter of a parallelogram the student should double the length of two adjacent sides, for a regular pentagon they should multiply the length of one side by five.
Students should connect the formulae for finding areas of parallelograms, triangles, and trapeziums to the formula for the area of a rectangle using partitioning and reassembling the shapes. Students should be able to find perimeters and areas of shapes where the side lengths are simple decimals in order to understand that area, in particular, is not restricted to discrete situations where the units of measure can be counted individually.