CoachThe area of a figure drawn on a grid is the number of grid squares it covers. Two half-squares count as one. Area answers “how much surface”, perimeter answers “how long is the border” — two different questions!
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Example 28.6 (Half-squares)
A right triangle drawn on the grid with legs and covers full squares and half-squares … count carefully: its area is half of the rectangle, i.e. squares. Cutting a rectangle along its diagonal always gives two triangles of equal area.
Example 28.7 (Same area, different perimeters)
A square and an rectangle both cover squares — same area. Borders: units for the square, for the rectangle. Neither measure determines the other: a long thin shape has lots of border for little surface.