Area of rectangles and squares

Now we move from perimeter to area. Perimeter is the distance round the edge; area is the space inside. The amount of region enclosed by a closed figure is called its area. We measure area in square units, such as square metres (sq m) or square centimetres (sq cm). Perimeter is written in plain cm or m; area is always in square units.

Why is the area of a rectangle length × width? Fill a rectangle 5 cm long and 3 cm wide with little squares of side 1 cm. There are 5 squares in each row and 3 rows, so 5 × 3 = 15 squares: the area is 15 sq cm.

• Area of a rectangle = length × width.
• Area of a square = side × side.

A floor 5 m long and 4 m wide has area 5 × 4 = 20 sq m. A square carpet of side 3 m has area 3 × 3 = 9 sq m. If the carpet is laid on that floor, the part not covered is 20 − 9 = 11 sq m.

The book's second example: four square flower beds, each of side 4 m, sit in the four corners of a piece of land 12 m long and 10 m wide. The whole land is 12 × 10 = 120 sq m. One bed is 4 × 4 = 16 sq m, so four beds are 4 × 16 = 64 sq m. The land left over is 120 − 64 = 56 sq m.

We can also work backwards. A rectangular garden 25 m long has area 300 sq m. Length × width = 300, so the width is 300 ÷ 25 = 12 m. And to share out space: a coconut grove 100 m long and 50 m wide has area 100 × 50 = 5000 sq m. If each tree needs 25 sq m, at most 5000 ÷ 25 = 200 trees can be planted.

Area helps with costs too. To tile a plot 500 m by 200 m (area 100,000 sq m) at ₹8 for every 100 sq m, count the lots of 100 sq m: 100,000 ÷ 100 = 1000 lots, so the tiling costs 1000 × ₹8 = ₹8000.