Counting of figures reasoning question is the most important part of reasoning topic. In most of the competitive exams, various types of questions asked from this topic like squares, rectangles, and triangle counting reasoning questions also Straightline counting figures reasoning questions, etc. today in this post you can get all types of counting of figures reasoning questions and answers with explanation also some important tips and tricks to solve counting of figures reasoning questions that help to solve an example of counting of figures reasoning questions in exam.

Introduction- counting of figures reasoning questions

Counting of figures is the type of nonverbal reasoning. counting of figures reasoning questions is the question that involves the mixture of two or more types of complex figures. it involves the various shape of a geometrical figure like triangle, square, rectangle, circle, straight line, etc. search types of questions and design to taste the analytical deposition of the candidates.

This chapter involves problems relating to the counting of the number of particular geometrical figures in a given Complex geometrical figure.  The understanding of this chapter will help us in attempting 2 to 5  questions in the examination.

Types of counting of figures reasoning

Mostly there are 4 types of counting of figures reasoning questions asked in competitive exams, Types of counting of figures are given below

1. Triangle counting reasoning questions
2. Rectangle counting reasoning questions
3. Square counting reasoning questions
4. Straightline counting reasoning questions

Tips and tricks to solve counting of figures reasoning questions

The trick to counting the number of triangles

• As the triangle figure is shown below, the figure is divided into 4 parts. but sometimes it can be divided 6 or 8 times also. So in this type of question, you should know the simple trick to solve triangle counting figures

so, first label the triangle number then, apply this simple method
i.e. 1 + 2 + 3 + 4 = 10
So, the total number of triangles is 10.

• As the triangle figure is shown below, which is divided into some parts and also divide some height in this case
  
  =(Addition of triangle part) x Heighest Height
  = (1 + 2 + 3 + 4) x 3
  = 30
  so, total number of triangles is 30.

The Trick To Counting The Number Of Rectangles

As the figure is shown given below, If in rectangle type question there is the number of rows and columns. so in that case apply these tricks

Addition of column number
i.e 1 + 2 + 3 = 6
Addition of row number
i.e. 1 + 2 + 3 = 6
So, the total number of rectangles
6 x 6 = 36
[This trick applicable in both conditions for (same & different number of rows and column)]

The Trick To Counting The Number Of Squares

• As the figure is shown given below, If in rectangle type question there is a different number of rows and columns. so in that case apply these tricks
  
  Total number of square or rectangle
  = (3 x 6) + (2 x 5) + (1 x 4)
  = 18 + 10 + 4
  = 32.

As the figure is shown given below, If in square type question there is the same number of rows and columns. So, in that case, apply the following tricks

above figure have 3 rows & 3 columns
So, total number of rectangle
= 1² + 2² + 3²
= 1 + 4 + 9
= 14.

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Counting Of figures Reasoning Questions And Answers

The chapter, Counting Of figures analytical reasoning involves the problem relating to the geometrical figures in a given Complex figure the Systematic method for the number of any particular type of figure by the analysis of the complex figure would from the example that are given below.

Square counting reasoning questions- Examples

Q1. How many squares are there in the figure given below?

A) 7
B) 5
C) 6
D) 4

View Answer and Solution 

Answer: (B)
Solution: 

When rows and columns are the same.
So, count the number of columns or row i.e 2
= 12 + 22
= 1 + 4
= 5

Q2. Count the number of squares in the following figure?

A) 18
B) 14
C) 10
D) 9

View Answer and Solution 

Answer: (B)
Solution: Method 1
label the figure as shown below

the simplest square is AEML, EFNM, FBGN, NGHO, MNOP, LMPK, KPJD, POIJ, and OHCI i.e 9 in number.
The squares are composed of four components each are AFOK, EBHP, LNID, and MGCJ i.e. 4 in number.
There is only one square i.e. ABCD  composed of nine components.
Thus,  there are 9+4+1=14 Squares in the figure.

Method 2:
Square having same row and same column i.e. 3. so,
= 12 +22+ 32
= 1 + 4 + 9= 14

Straightline counting figures reasoning questions

Q3. What is the number of straight lines in the following figure?

A) 10
B) 12
C) 13
D) 17

View Answer and Solution 

Answer: (B)
Solution: label the figure as shown below:

clearly in this figure:
There are 3 horizontal lines namely AG, BF, and CE.
There are 3 vertical lines namely AC, HD, and GE.
There are 6 slanting lines namely AD, AE, GC, GD, CD, AND CE.
Thus, There are 3+3+6=12  straight lines in all.

Triangle counting reasoning questions with answers

Q4. How many Triangles are there in a given figure?

A) 28
B) 24
C) 25
D) 26

View Answer and Solution 

Answer: (A)
Solution: The figure in the question has been labeled as under naming the figure Clearly,  there are 28 Triangles in the given figure there are:

EOF, AOE, AOB, BOF, ABF, BEF, ABE, AEF, BPF, FPG, CPG, BPC, BFG, BCG, CFG, BCF, GQC, CDQ, DHQ, GDC, GDH, GHC, CDH, AFC, BCD, EBG, FCH.

Q5.  How many Triangles are there in the following figure?

A) 6
B) 10
C) 11
D) 12

View Answer and Solution 

Answer: (D)
Solution: The figure may be labeled As shown below:

The simplest triangle is ABE, BEF, EFC, CDE, AND AED i.e. 5 In number.
The Triangles are composed of two components each are ABF, BCE, ACE, and ABD i.e. 4 In number.
The triangles are composed of three components each being AFC  H and BCD i.e. 2 in number.
There is only one Triangle ABC  composed of five components. Thus 5+4+2+1 =12 Triangles in the figure.

About the author

Hi,
I am Vaibhav Choudhary, Reasoning Teacher by Profession but Blogger by a passion. I would like to share my reasoning knowledge with students those are taking a preparation of government exam or competitive exam.