Area by counting squares — Mathematics, 7–10 years
Area tells how much flat space a shape covers. Covering a shape with equal squares shows why multiplying rows by columns is a quick way to find it.
How much space inside?
Area is the amount of flat surface inside a shape. If a rectangle is covered exactly by 12 small squares, its area is 12 square units. The squares must touch with no gaps or overlaps, so the count is fair.
Why measure area?
Length alone cannot tell whether a floor needs one small tile or many. Area was needed to compare surfaces and plan materials such as tiles, paper or paint. Counting equal squares gives every surface the same kind of unit.
A rectangle of 3 by 5
Draw a rectangle 5 squares long and 3 squares wide. Count the first row: 5 squares; repeat it for three rows: 5 + 5 + 5 = 15. Therefore its area is 15 square units, which we can write as 5 × 3 = 15.
Area is not the edge
A common mix-up is to count only the squares along the outside edge. That counts around the shape, not the space inside it. A 4-by-3 rectangle has area 12 square units, even though its outline has only 10 unit edges.
Tiles, posters and gardens
Area helps decide how many tiles cover a floor, how much paper a poster needs or how much soil fits in a garden bed. The answer depends on the unit: square centimetres suit a small drawing, while square metres suit a room.
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