- Home/
- CDS & Defence/
- Article
How many squares are there in the given figure?
By BYJU'S Exam Prep
Updated on: September 25th, 2023
(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:
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.
