Question

In the given figure, if the centres of all the circles are joined by horizontal and vertical lines, then find the number of squares that can be formed.

• A. 6
• B. 7
• C. 8
• D. 1

Answer 1

The Correct Option is C

To find the number of squares that can be formed by joining the centers of the circles, let us first analyze the arrangement:

The circles are arranged in a 3x4 grid. The centers of the circles form points on a grid where squares can be formed. Let’s calculate the number of squares:

1. Identify single-unit squares:
   • You can form single-unit (1x1) squares by selecting four adjacent circle centers. Since the grid is 3x4, you can form 2 squares horizontally and 2 squares vertically for each row and column of centers.
   • Total 1x1 squares = 2 (horizontal) x 3 (rows) + 3 (vertical) x 2 (columns) = 6.
2. Identify double-unit squares:
   • You can form double-unit (2x2) squares by selecting four points that cover two units horizontally and two units vertically.
   • There can only be one such 2x2 square, formed in the middle.
   • Total 2x2 squares = 1.
3. Identify full grid squares (3x3):
   • Forming one large square by covering three points on one side and three on its adjacent side.
   • This is possible in the center, encompassing most of the grid.
   • Total 3x3 squares = 1.

Adding all these together, we get: 6 (1x1) + 1 (2x2) + 1 (3x3) = 8 squares.

Therefore, the number of squares that can be formed is 8.