In the given figure, dots in rows and columns make a rectangle. Did you count the dots one by one?

Given: Dots in rows and columns make a rectangle. Here, to find the total number of dots we need not count each dot, we can count number of dots in a row and multiply that to number of rows. In the given figure, there are 4 rows and in each row there are 6 dots. Therefore, total number of dots in all the 4 row is 4 × 6 = 24 No, we need not count each dot.

In the given figure, dots in rows and columns make a rectangle. Can you make other rectangles with 24 dots? Is any one of these rectangles a square?

Rectangular array: An arrangement of objects into rows and columns that form a rectangle. In given rectangular array there are 24 dots, we need make similar kind of rectangles using 24 dots. That is, This rectangular array can be represented as 2 × 12 Number of rows × Number of columns This rectangular array can be represented as 3 × 8 Number of rows × Number of columns This rectangular array can be represented as 8 × 3 Number of rows × Number of columns This rectangular array can be represented as 6 × 4 Number of rows × Number of columns Therefore, 2 × 12 and 6 × 4 are two rectangles with 24 dots. Here, both the figures are not squares, because in square the number of row must be equal to number of columns. Hence, the obtained figures are not squares.

In the given figure, dots in rows and columns make a rectangle. Can you remove some dots and make a square? How many?

The given rectangular grid has 24 dots, it has 4 rows and 6 columns. We know that, in square array number rows and number of columns must be equal i.e., n × n To make the given rectangular array into the square array we need to remove 2 columns each contains 4 dots. Then, each row and column contains same number of dots. That is, Here, the square array we can be represented as 4 × 4 . Therefore, we need to remove 8 dots to make given rectangle into square.