8. A square field has a side length of 4 units. (i) What is its area? (ii) What is its perimeter? (iii) If the field can be rectangular, is it possible to keep the value of the area you have found above, but change the total size of the perimeter? If possible, give an example.
(iv) Draw a diagram of the ‘new’ field and explain your answer. (Note: total area must still equal 16 square units.)
(v)
If the area of the field must remain at 16 square units, how many different values of the perimeter are there? Justify your answers using diagrams. (Note: you may only use natural numbers for length and width.) (a) What is the largest perimeter? (b) What is the smallest perimeter?
(vi) Is the following statement true or false? ‘If the area of a rectangular shape remains unchanged, you cannot change the length of the perimeter.’ Give a reason for (justify) your answer.