Counting squares

In your book, Maths Mela (Chapter 11), there are three rectangles, A, B and C, and we want to know which has the largest area. It is hard to tell just by looking. So we put them on a square grid and count the squares each one covers.

Rectangle A is 3 squares wide and 4 squares tall, so it covers 12 squares. Rectangle B is 2 squares wide and 4 squares tall: 8 squares. Rectangle C is 2 squares wide and 5 squares tall: 10 squares. So A has the largest area, then C, then B. A square grid is the easiest way to compare areas. A square whose sides are 1 unit long has an area of 1 unit square. On a grid of 1 cm squares, each square is 1 square cm.

The book also compares two gardens on a 1 cm grid. Garden A is 2 cm wide and 5 cm long, so it covers 10 squares: 10 square cm. Garden B is 4 cm wide and 3 cm long, so it covers 12 squares: 12 square cm. Garden B has the bigger area, even though Garden A is longer.

Some shapes cover half squares. Then we count two half squares as one whole square. The book shows a square 3 squares wide and 3 tall, which covers 9 squares, and a triangle 6 squares wide at the top that narrows to a point 3 squares down. Counting its whole squares and putting its half squares together in twos, the triangle also covers 9 squares. So the two shapes have the same area, though they look very different.