(i) You can probably see straight away how you could use two straight, perpendicular lines to divide a square into four pieces of equal area. But how many ways are there to do this?

(ii) A slightly trickier problem arises if we have to use two straight, perpendicular lines to divide an equilateral triangle into four pieces of equal area. Find a way to do this and describe precisely where to draw the two straight lines.

(iii) More challenging still! Find a way to use two straight, perpendicular lines to divide a regular pentagon into four pieces of equal area and describe precisely where to draw the two straight lines.