Area by tiling

In your book, Maths Mela (Chapter 11), Preetha and Adrit try to cover their table tops with shapes. Preetha uses triangles on one table and circles on another. Adrit uses squares on one table and rectangles on another.

The triangles, the squares and the rectangles cover the table top with no gaps and no overlaps: they fit together edge to edge, like floor tiles. We say these shapes tile. The circles do not tile: however you arrange them, gaps are left between them. The region covered by the tiles is called the area of the table top.

We can give an area by counting tiles. Suppose a table top is covered exactly by 12 squares. Its area is 12 square units. If each of those squares is cut in half into 2 triangles, 24 triangles cover the same table, so its area is also 24 triangle units. The table has not changed; only the unit has.

Preetha also covers her desk with tiles. It is 9 squares long and 6 squares wide, so it has 6 rows of 9 squares: 9 × 6 = 54 blue squares cover it. A green triangle is half of a blue square, so it takes 2 green triangles for each square: 54 × 2 = 108 green triangles cover the desk.