Area

Area is the amount of surface a flat shape covers, measured in square units. A square centimetre is a square one centimetre on each side. Saying that a rectangle has an area of 12 without a unit, or with a plain centimetre, loses the point of the measurement.

Counting squares

Before any formula, area is a count. Draw a shape on grid paper and count the squares inside it. A rectangle 5 squares across and 3 squares down holds 15 squares, and the multiplication 5 x 3 is a shortcut for counting them.

Shapes that do not fit the grid

For a shape whose edges cut across squares, count the whole squares first, then pair up the part squares. Two halves make a whole. This is rough, and it is meant to be: it builds the intuition that a triangle sitting inside a rectangle covers about half of it, which is where the triangle formula comes from.

Area is not perimeter

Same perimeter, very different areas. Perimeter measures the distance around a shape, in ordinary units. Area measures the surface inside, in square units. Of all rectangles with a given perimeter, the square holds the most area, which is worth discovering on grid paper rather than being told.

Shapes made of rectangles

Common mistakes

Leaving off the square

Area is always in square units. Writing 44 metres for the area of a room describes a distance, not a floor.

Adding the sides

Adding length and width gives half the perimeter, not the area. Area multiplies.

Check yourself