How many squares are there in the given figure?

By Raj Vimal|Updated : October 20th, 2022

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(A) 16

(B) 17 

(C) 26

(D) 30

There are 30 squares in the given figure. The figure above has 4 rows and 4 columns. Let n, therefore, equal 4. Here, we'll use the following formulas to determine how many squares there are in a n x n grid. n² + (n - 1)² + (n - 2)² + - - - - - - - - - - + (n - n)²

A matrix with four by four squares has four squares.

= 4² + 3² + 2² + 1²

= 16 + 9 + 4 + 1 

= 30

As illustrated below, let us assign a number in each block of the square in order to count it:

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Sqaures which involves only one block = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16} = 16 squares

Squares which involves four blocks = {(1, 2, 5, 6), (2, 6, 3, 7), (3, 7, 4, 8), (5, 6, 9, 10), (6, 7, 10, 11), (7, 8, 11, 12), (9, 10, 13, 14), (10, 11, 14, 15), (11, 12, 15, 16)} = 9 squares

Squares which involves 9 blocks = {(1, 2, 3, 5, 6, 7, 9, 10, 11), (2, 3, 4, 6, 7, 8, 10, 11, 12), (5, 6, 7, 9, 10, 11, 13, 14, 15), (6, 7, 8, 10, 11, 12, 14, 15, 16)} = 4 squares

Squares which involves 16 blocks = 1

Total number of squares = 16 + 9 + 4 + 1 = 30 squares.

Therefore, the depicted figure contains 30 squares.

The best answer is hence "30."

Summary:

How many squares are there in the given figure? (A) 16 (B) 17 (C) 26 (D) 30

There are 30 squares in the given figure and the figure above has 4 rows and 4 columns. The given figure will help you to solve the question easily. 

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