I'd also recommend revisiting part (ii), as you got that answer wrong. You said that the distance between the North Gate and the South Gate is 3600 m
2 which means that that distance would be represented by 9 squares on the grid. But how did you come to
that conclusion? Even using the naive (and incorrect) approach of saying that you have to go 5 squares down and 3 squares to the right, that produces a "distance" of 8 squares, not 9.
If you label the bottom left corner of the grid (0,0), then the coordinates of North Gate are (3, 6) and the coordinates of the South Gate are (6, 1). What does the
distance formula indicate about the distance between these two points? Can you see why it must be less than 8 squares, because travelling along the diagonal must be a shorter path than walking the two straight lines?
Regarding the area of the shape, one way of generating a crude estimate is to count the number of whole squares inside the shape, then add an additional one-half square for any square where
any portion is inside the square (so even the two squares on the left side that only a sliver is inside the shape would still count as 1/2 each). Doing this shows there are 17 whole squares and 18 half-squares, giving an estimate of the area as 26 squares. The reason this estimate works reasonably well is because it over-estimates the area of the squares where only a sliver is inside, but under-estimates the area of the squares that are almost fully contained within the shape, and in the end these errors roughly cancel out.
