Figure Counting: Meaning, Reasoning Questions with Answers, Formula

Figure counting is a popular topic in reasoning exams that tests your ability to identify and count specific shapes hidden within a complex diagram. Whether it’s triangles, squares, rectangles, or other geometric patterns, these figure counting questions require sharp observation and a systematic approach. Many aspirants look for counting figure tricks to solve triangle counting questions with answers quickly and accurately. Mastering counting figures reasoning not only improves speed but also reduces errors in competitive tests. As part of logical reasoning, this topic plays a crucial role in assessing analytical thinking and problem-solving ability. From basic counting of figures exercises to challenging counting figures questions involving overlapping shapes, it demands both logic and consistent practice. In this article, we will explore techniques, solved examples, and step-by-step strategies to tackle all types of counting of figures reasoning questions effectively. These questions will help you score better in the figure counting problems in various exams such as BITSAT, MAH MBA CET, SSC, railways and other competitive exams.

This Story also Contains

1. Approach to Solve the Questions Based on Figure Counting Reasoning
2. Types of Questions Asked from the Figure Counting Reasoning
3. Non-Verbal Reasoning Topics
4. Recommended Books and Online Resources for Figure Counting
5. Question Weightage of Counting of Figure Reasoning Questions in Competitive Exams
6. Figure Counting Tricks to Solve the Counting of Figure Reasoning Questions
7. Practice Questions For Counting the Squares
8. Practice Questions For Counting the Rectangles
9. Practice Questions For Counting the Triangles
10. Practice Questions For Counting the Quadrilaterals
11. Figure Counting Questions for BITSAT/ CUET
12. Figure Counting Questions for SSC CGL/ SSC CHSL/ SSC CPO/ SSC Stenographer exams
13. Figure Counting Questions for Railway Recruitment Board - RRB Exams
14. Previous Year Questions of Figure Counting in Various Exams
15. Preparation Tips for Figure Counting
16. Verbal Reasoning Topics

Approach to Solve the Questions Based on Figure Counting Reasoning

To solve questions related to figure counting, reasoning, follow the steps below:

1) The first step is to identify which figure has to count, such as a triangle, a rectangle, a square, a quadrilateral, etc.

2) Let’s assume that a counting figure question asks to find the number of triangles in the given figure. For this, we have to label the figure and then point out the different vertices that make the complete triangles together.

3) The third step is to start counting the figures from the bigger ones.

4) After labelling, we will be able to identify the different triangles and track the number of triangles in the figure. The same needs to be followed for other shapes as well.

Types of Questions Asked from the Figure Counting Reasoning

The topic of figure counting reasoning is divided into various parts based on the counting of different shapes, and they are as follows -

1. Count the total number of Squares

2. Count the total number of rectangles

3. Count the total number of triangles

4. Count the total number of quadrilaterals

Let’s discuss these types and figure counting formulas in detail with the help of examples -

1. Count the Total Number of Squares

In this type, we have to count the total number of squares in the given adjoining figure. For this, label the given adjoining figure, and point out the different vertices that together make the complete square. By using these vertices, we can count the number of squares in the given figure. Let’s understand this with the help of an example.

Example: Consider the diagram given below and count the number of squares.

To count the number of squares in the above adjoining figure, first, we have to label the figure and then count the number of squares. The given figure can be labelled as shown below:

The squares in the above figure are - QYUW, WUXT, YRVU, UVSX, QRST, IJUP, PUNO, ULMN, JKLU, IKMO, GFUH, HUBA, UDCB, FEDU, and GECA. Thus, there are a total of 15 squares in the above figure.

2. Count the Total Number of Rectangles

In this type, we have to count the total number of rectangles in the given adjoining figure. For this, label the given adjoining figure, and point out the different vertices that together make the complete rectangle. By using these vertices, we can count the number of rectangles in the given figure. However, while counting the number of rectangles, we have to consider the squares as well. All squares can be rectangles but all rectangles cannot be squares. Therefore, in the counting of rectangles, we have to count the number of squares in the given figure. Let’s understand this with the help of an example.

Example: Consider the diagram given below and count the number of rectangles.

To count the number of rectangles in the above adjoining figure, first, we have to label the figure and then count the number of rectangles. The given figure can be labelled as shown below:

The rectangles in the above figure are - ABCD, EFGH, IJKL, MFNQ, EMQR, EFNR, QNOD, NJPO, QJPD, RNGH, MFOD. Thus, there are a total of 11 rectangles in the above figure.

3. Count the Total Number of Triangles

In this type, we have to count the total number of triangles in the given adjoining figure. For this, label the given adjoining figure, and point out the different vertices that together make the complete triangle. By using these vertices, we can count the number of triangles in the given figure. Let’s understand this with the help of an example.

Example: Consider the diagram given below and count the number of triangles.

To count the number of triangles in the above adjoining figure, first, we have to label the figure and then count the number of triangles. The given figure can be labelled as shown below:

The triangles in the above figure are - AFE, EDG, EFG, EHN, HNM, EHM, HIJ, GML, GNK, and HKL. Thus, there are a total of 10 triangles in the above figure.

4. Count the Total Number of Quadrilaterals

In this type, we have to count the total number of Quadrilaterals in the given adjoining figure. For this, label the given adjoining figure, and point out the different vertices that together make the complete quadrilaterals. By using these vertices, we can count the number of quadrilaterals in the given figure. However, while counting the number of quadrilaterals, we have to consider the squares and rectangles as well. All the four-sided enclosed figures are quadrilaterals, irrespective of the shape. Let’s understand this with the help of an example.

Example: Consider the diagram given below and count the number of quadrilaterals.

To count the number of quadrilaterals in the above adjoining figure, first, we have to label the figure and then count the number of quadrilaterals. The given figure can be labelled as shown below:

The quadrilaterals in the above figure are - ABFE and ABCE. Thus, there are a total of 2 quadrilaterals in the above figure.

Non-Verbal Reasoning Topics

Non-verbal reasoning topics assess your ability to analyze and interpret visual information without using words or numbers. These include non-verbal analogy reasoning, figure series reasoning, classification, embedded figures, cube and dice reasoning, mirror and water images, and completion of figures, all of which enhance pattern recognition and problem-solving skills. The important non-verbal reasoning topics are given below:

Recommended Books and Online Resources for Figure Counting

Recommended books and online resources for figure counting provide the right mix of theory, solved examples, and practice questions to strengthen your skills. These resources help aspirants master counting of figures reasoning questions with speed and accuracy.

Question Weightage of Counting of Figure Reasoning Questions in Competitive Exams

The number of counting of figures reasoning questions asked in competitive exams can vary depending on the exam type and difficulty level. These questions are generally quick to attempt if practiced well, making them a scoring topic for candidates.

• SSC Exams (SSC MTS, SSC CGL, SSC CHSL, SSC CPO, Stenographer): Usually 2 to 3 questions are asked, often involving triangle counting or mixed shape diagrams.

• RRB Exams (Group D, NTPC, JE, ALP, etc.): Around 2 to 3 questions are common, typically based on basic counting figures reasoning with moderate complexity.

• Banking Exams (Bank PO, Bank Clerk): Generally 1 to 2 questions are asked, often straightforward but requiring accuracy under time pressure.

Figure Counting Tricks to Solve the Counting of Figure Reasoning Questions

1. Count the Number of Squares and Rectangles

To count the number of squares and rectangles in a figure, firstly, we have to number the divided parts in the figure as shown below.

To determine the number of squares, multiply the last number in the row by the last number in the column and then multiply the numbers after subtracting 1 from both numbers. Continue the procedure until one of the two numbers becomes 1, and then add all the resultant numbers to get the number of squares.

Number of squares $= (6 \times 3) + (5 \times 2) + (4 \times 1) = 18 + 10 + 4 = 32$

In the above figure, there are a total of 32 squares.

To determine the number of rectangles, multiply the sum of the numbers in the first row and the sum of the numbers in the first column.

Number of total rectangles $= (1 + 2 + 3 + 4 + 5 + 6) \times (1 + 2 + 3) = 21 \times 6 = 126$

In the above figure, there are a total of 126 rectangles. (These rectangles also include the count of squares, because all squares are rectangles, but all rectangles are not squares.)

There is one more figure-counting trick to calculate the number of squares and rectangles in a square (when the number of rows is equal to the number of columns):

The number of squares $= \frac{n(n + 1)(2n + 1)}{6}$

The number of rectangles $= \left(\frac{n(n + 1)}{2}\right)^2$

Here, $n = 6$

So, the total number of squares $= \frac{6 \times 7 \times 13}{6} = \frac{546}{6} = 91$

The total number of rectangles $= \left(\frac{6 \times 7}{2}\right)^2 = \left(\frac{42}{2}\right)^2 = 21^2 = 441$ (Squares are also included)

NOTE: But, in case, if the question asks “only rectangles” instead of “total rectangles”, then subtract the number of squares from the total number of rectangles.

2. Count the Number of Triangles

Let’s consider some figures of the triangle of a common type.

In these types of triangles, we will count the total number of triangles on the basis of the number of bases in each triangle. In the first figure, we have 2 bases, in the second figure, we have 3 bases, and in the third figure, we have 4 bases. Let us consider that ‘n’ denotes the number of bases.

So, the total number of triangles $= \frac{n(n + 1)}{2}$

The number of triangles in the first figure $= \frac{2(2 + 1)}{2} = \frac{6}{2} = 3$

The number of triangles in the first figure $= \frac{3(3 + 1)}{2} = \frac{12}{2} = 6$

The number of triangles in the first figure $= \frac{4(4 + 1)}{2} = \frac{20}{2} = 10$

Here, the triangles can also be divided horizontally as shown below:

Here, the first step is the same as we did before, but after that step here we will multiply that by the number of horizontal parts.

As we can see, in the first figure, there are 2 horizontal parts, and in the second figure, there are 3 horizontal parts.

So, the number of triangles in the first figure $= 2 \times \left(\frac{2(2 + 1)}{2}\right) = 2 \times \left(\frac{6}{2}\right) = 2 \times 3 = 6$

So, the number of triangles in the second figure $= 3 \times \left(\frac{4(4 + 1)}{2}\right) = 3 \times \left(\frac{20}{2}\right) = 3 \times 10 = 30$

Now, let’s consider the triangles of another form.

As, in the above figures, we can see a big triangle is divided into a number of small triangles. To count the number of triangles in the above figures, we have to determine the number of bases in the given figure and then apply the required formula. Let us consider that ‘n’ denotes the number of bases.

In the first figure, there are 2 bases, in the second figure, there are 3 figures, in the third figure, there are 4 bases, and in the fifth figure, there are 5 bases. So, the number of bases is even as well as odd. Based on the number of bases (either odd or even), there are 2 formulas.

So, the total number of triangles (when the number of bases is even) $= \frac{n(n + 2)(2n + 1)}{8}$

So, the total number of triangles (when the number of bases is odd) $= \frac{n(n + 2)(2n + 1) - 1}{8}$

For the first figure, $n = 2$ (Even)
So, the total number of triangles $= \frac{2(2 + 2)(2(2) + 1)}{8} = \frac{2 \times 4 \times 5}{8} = 5$

For the second figure, $n = 3$ (Odd)
So, the total number of triangles $= \frac{3(3 + 2)(2(3) + 1) - 1}{8} = \frac{(3 \times 5 \times 7) - 1}{8} = \frac{104}{8} = 13$

For the third figure, $n = 4$ (Even)
So, the total number of triangles $= \frac{4(4 + 2)(2(4) + 1)}{8} = \frac{4 \times 6 \times 9}{8} = 27$

For the fourth figure, $n = 5$ (Odd)
So, the total number of triangles $= \frac{5(5 + 2)(2(5) + 1) - 1}{8} = \frac{(5 \times 7 \times 11) - 1}{8} = \frac{384}{8} = 48$

3. Count the Number of Triangles in a Square or Rectangle

If we have to count the number of triangles in a square or a rectangle, then just simply multiply the total number of parts in the figure by 2 to get the required answer. The example is as follows:

Here, in the above figure, there are a total of 8 parts of a square.

So, the total number of triangles = 2 × 8 = 16

For more practice, follow the figure counting questions below with answers of each type:

Practice Questions For Counting the Squares

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

A) 10

B) 11

C) 12

D) 14 (Correct)

Solution: Label the given figure and then count the number of squares. The given figure can be labelled as shown below:

The squares in the above figure are - ABCP, PCQO, OQRN, NRLM, CDEQ, QESR, RSKL, EFGS, SGJK, GHIJ, PDSN, OEKM, QFJL and NLSQ. Thus, there are 14 squares in the above figure. Hence, the fourth option is correct.

Q2. Directions: How many squares are there in the given figure?

A) 8

B) 14

C) 10 (Correct)

D) 12

Solution: Label the given figure and then count the number of squares. The given figure can be labelled as shown below:

The squares in the above figure are - ABIH, HIFG, BCDI, IDEF, JKLM, JOIN, OKPI, IPLQ, NIQM, and ACEG. Thus, there are 10 squares in the above figure. Hence, the third option is correct.

Q3. Directions: How many squares are there in the given figure?

A) 28 (Correct)

B) 54

C) 53

D) 27

Solution: Label the given figure and then count the number of squares. The given figure can be labelled as shown below:

The squares in the above figure are - ABIH, HION, BCJI, OIJP, ACPN, DKLE, ELMF, KLRQ, LRSM, DQSF, FSTG, QSZY, ZSTa, YDGa, eUVf, fbcr, rcdg, VbcW, WcdX, fVXg, lefm, mfgn, hiks, iktj, oskp, pktq, ohjq, and lUXn. Thus, there are 28 squares in the above figure. Hence, the first option is correct.

Q4. Directions: How many squares are there in the given figure?

A) 26

B) 30

C) 35 (Correct)

D) 38

Solution: Label the given figure and then count the number of squares. The given figure can be labelled as shown below:

The squares in the above figure are - ABQP, BCXQ, CXRD, DRFE, POSQ, SQXT, TXRU, RUGF, OSVN, VSTY, YTUW, WUGH, NMLV, LKYV, KYWJ, JIHW, ACTO, BDUS, CTGE, NPXY, VQRW, YXFH, MOTK, LSUJ, KTGI, NADW, VBEH, MPRJ, LQFI, AEIM, KOCG, VOQT, TQCR, TRGW, and KVTW. Thus, there are 35 squares in the above figure. Hence, the third option is correct.

Q5. Directions: How many squares are there in the given figure?

A) 11

B) 12

C) 10 (Correct)

D) 9

Solution: Label the given figure and then count the number of squares. The given figure can be labelled as shown below:

The squares in the above figure are - LMNO, EFGH, EJIT, TIKH, JFUI, IUGK, LPIR, RIQO, IPMS, and ISNQ. Thus, there are 10 squares in the above figure. Hence, the third option is correct.

Practice Questions For Counting the Rectangles

Q1. Directions: How many rectangles are there in the given figure?

A) 8

B) 5

C) 9 (Correct)

D) 4

Solution: Label the given figure and then count the number of rectangles. The given figure can be labelled as shown below:

The rectangles in the above figure are - AEOH, EBFO, OFCG, HOGD, ABFH, HFCD, AEGD, EBCG, and ABCD. Thus, there are 9 rectangles in the above figure. Hence, the third option is correct.

Q2. Directions: How many rectangles are there in the figure ABCD?

A) 11

B) 12

C) 9

D) 10 (Correct)

Solution: Label the given figure and then count the number of rectangles. The given figure can be labelled as shown below:

The rectangles in the above figure are - AEJF, EBIJ, KICH, NGDH, KLMN, FGML, FGNK, ABCD, AFIB, and FDCI. Thus, there are 10 rectangles in the above figure. Hence, the fourth option is correct.

Q3. Directions: How many rectangles are there in the given figure?

A) 8

B) 5

C) 6 (Correct)

D) 4

Solution: Label the given figure and then count the number of rectangles. The given figure can be labelled as shown below:

The rectangles in the above figure are - ABDC, CDFE, ABFE, ONGF, MLJK, and GKIH. Thus, there are 6 rectangles in the above figure. Hence, the third option is correct.

Q4. Directions: How many rectangles are there in the given figure?

A) 9 (Correct)

B) 7

C) 8

D) 10

Solution: Label the given figure and then count the number of rectangles. The given figure can be labelled as shown below:

The rectangles in the above figure are - ABCF, CDEF, ABDE, MNGL, LGHK, KHIJ, MNHK, MNIJ, and LGIJ. Thus, there are 9 rectangles in the above figure. Hence, the first option is correct.

Q5. Directions: How many rectangles are there in the given figure?

A) 6

B) 7

C) 8

D) 9 (Correct)

Solution: Label the given figure and then count the number of rectangles. The given figure can be labelled as shown below:

The rectangles in the above figure are - ABJI, BJLC, CDEK, EFGK, GHIL, ACGH, AHFD, AILC, and CDFG. Thus, there are 9 rectangles in the above figure. Hence, the fourth option is correct.

Practice Questions For Counting the Triangles

Q1. Directions: How many triangles are there in the given figure?

A) 24

B) 30

C) 28 (Correct)

D) 29

Solution: To solve the figure counting triangle reasoning questions, label the given figure and then count the number of triangles. The given figure can be labelled as shown below:

The triangles in the above figure are - AFG, AEG, AFE, BFJ, BDJ, BFD, CEI, CDI, CED, ABD, ACD, ABC, AHB, AHE, DEF, DEG, DFG, GHE, DEH, JHD, BEC, BHD, AEB, AFD, AED, DJE, FEJ, and BDE. Thus, there are 28 triangles in the above figure. Hence, the third option is correct.

Q2. Directions: How many triangles are there in the given figure?

A) 8

B) 10

C) 12 (Correct)

D) 14

Solution: To solve the figure counting triangle reasoning questions, label the given figure and then count the number of triangles. The given figure can be labelled as shown below:

The triangles in the above figure are - ADE, BCF, AJD, DJC, CJB, BJA, ADC, DCB, CBA, BAD, EAC, and DBF. Thus, there are 12 triangles in the above figure. Hence, the third option is correct.

Q3. Directions: How many triangles are there in the given figure?

A) 4

B) 5

C) 7

D) 6 (Correct)

Solution: To solve the figure triangle counting questions, label the given figure and then count the number of triangles. The given figure can be labelled as shown below:

The triangles in the above figure are - ABC, DEF, GHI, JKC, MNC, and LOF. Thus, there are 6 triangles in the above figure. Hence, the fourth option is correct.

Q4. Directions: How many triangles are there in the given figure?

A) 9

B) 10

C) 11

D) 8 (Correct)

Solution: To solve the figure triangle counting questions, label the given figure and then count the number of triangles. The given figure can be labelled as shown below:

The triangles in the above figure are - AEF, GBH, ICJ, LDK, MNO, ONQ, MOQ, and MPQ. Thus, there are 8 triangles in the above figure. Hence, the fourth option is correct.

Q5. Directions: How many triangles are there in the given figure?

A) 20

B) 21

C) 22

D) 24 (Correct)

Solution: To solve the figure counting triangle reasoning questions, label the given figure and then count the number of triangles. The given figure can be labelled as shown below:

The triangles in the above figure are - ABJ, AIJ, IJK, BJK, ILF, FLE, LEK, ILK, BCK, CKD, KDE, AHI, HIG, GIF, AIK, BIK, IEF, KFE, IKF, IKE, ABK, AIB, AKF, and BIE. Thus, there are 24 triangles in the above figure. Hence, the fourth option is correct.

Practice Questions For Counting the Quadrilaterals

Q1. Directions: How many quadrilaterals are there in the given figure?

A) 17 (Correct)

B) 15

C) 14

D) 21

Solution: Label the given figure and then count the number of quadrilaterals. The given figure can be labelled as shown below:

The quadrilaterals in the above figure are - AFKE, FBGK, EKHD, KGCH, ABGE, EGCD, AFHD, FBCH, ABCD, AFJD, FBCJ, EKJD, KGCJ, ABIE, FBIK, EICD, and KICH. Thus, there are 17 quadrilaterals in the above figure. Hence, the first option is correct.

Q2. Directions: How many quadrilaterals are there in the given figure?

A) 7

B) 6 (Correct)

C) 4

D) 8

Solution: Label the given figure and then count the number of quadrilaterals. The given figure can be labelled as shown below:

The quadrilaterals in the above figure are - ADFE, FEBC, ADCE, BCFA, AFCE, and ABCD. Thus, there are 6 quadrilaterals in the above figure. Hence, the second option is correct.

Q3. Directions: How many quadrilaterals are there in the given figure?

A) 16 (Correct)

B) 17

C) 15

D) 14

Solution: Label the given figure and then count the number of quadrilaterals. The given figure can be labelled as shown below:

The quadrilaterals in the above figure are - ABOK, BCPO, CDER, ERGF, GHNQ, JNHI, JKLM, LPQM, KPQJ, IJQG, ACPK, CDFG, ADFI, ACGI, KPGI, and ACQJ. Thus, there are 16 quadrilaterals in the above figure. Hence, the first option is correct.

Q4. Directions: How many quadrilaterals are there in the given figure?

A) 15

B) 16

C) 14 (Correct)

D) 13

Solution: Label the given figure and then count the number of quadrilaterals. The given figure can be labelled as shown below:

The quadrilaterals in the above figure are ABML, KLMN, ABNK, BCDN, ACDK, DEJK, EFPO, FGHP, EGHO, OHIJ, EGIJ, ACGI, ACEJ, and GIKD. Thus, there are 14 quadrilaterals in the above figure. Hence, the third option is correct.

Q5. Directions: How many quadrilaterals are there in the given figure?

A) 21

B) 22

C) 24 (Correct)

D) 23

Solution: Label the given figure and then count the number of quadrilaterals. The given figure can be labelled as shown below:

The quadrilaterals in the above figure are - AEFO, AEGP, AEHD, OFGP, OFHD, PGHD, ABMO, EBMF, OIJP, OMNP, FIJG, FMNG, IMNJ, PKLD, PNCD, GKLH, GNCH, KNCL, EBNG, EBCH, FMCH, ABNP, ABCD, and OMCD. Thus, there are 24 quadrilaterals in the above figure. Hence, the third option is correct.

For more questions, you must practice from the figure counting questions PDF or download the e-book of figure counting questions with answers PDF given below:
Figure Counting Questions with Solutions PDF

Figure Counting Questions for BITSAT/ CUET

In entrance exams such as BITSAT and CUET, generally 1 - 2 questions are asked, which the candidate can solve easily if they practice several questions based on the figure counting reasoning.

1) Directions: How many rectangles are there in the given figure?

1) 9

2) 10

3) 11

4) 12

Solution

The given figure can be labelled as shown below –

There are a total of 11 rectangles in the above figure. They are ABCD, EFGH, IJKL, MFNQ, EMQR, EFNR, QNOD, NJPO, QJPD, RNGH, MFOD.

Hence, the third option is correct.

Figure Counting Questions for SSC CGL/ SSC CHSL/ SSC CPO/ SSC Stenographer exams

1) Directions: How many triangles are there in the given figure?

1) 11

2) 9

3) 10

4) 12

Solution

The given figure can be labelled as shown below –

There are a total of 10 triangles in the above figure. They are AFE, EDG, EFG, EHN, HNM, EHM, HIJ, GML, GNK, HKL.

Hence, the third option is correct.

2) Directions: How many triangles are there in the given figure?

1) 28

2) 36

3) 40

4) 48

Solution

The figure can be labelled as shown below –

There are a total of 36 triangles in the above figure. They are AEI, IEB, BJF, CJF, DKG, CKG, HAL, DHL, AEB, BFC, CGD, DHA, AML, LMD, DMK, KMC, CMJ, JMB, BMI, IMA, AMD, DMC, CMB, BMA, ADC, DCB, CBA, BAD, HAM, HDM, MBF, MCF, MDG, MCG, MAE, MBE.

Hence, the second option is correct.

Figure Counting Questions for Railway Recruitment Board - RRB Exams

1) Directions: How many triangles are there in the given figure?

1) 10

2) 11

3) 12

4) 13

Solution

The figure can be labelled as shown below –

There are 11 triangles in the above figure. They are ABC, AGB, AGC, DBF, DFG, DBG, GEH, HEC, GEC, ADG, AEG.

Hence, the second option is correct.

Previous Year Questions of Figure Counting in Various Exams

1) Directions: How many triangles are there in the given figure?

1) 22

2) 21

3) 16

4) 24

Hint: To solve the reasoning triangle questions, firstly, label the given figure and determine the total number of triangles contained within it.

Solution

The given figure can be labelled as shown below –

In the above-labelled figure, there are a total of 22 triangles. They are AKM, ADH, HNM, HEA, HNO, HEF, HMO, HAF, FOP, FHI, FPQ, FIJ, FOQ, FHJ, JRQ, JGF, JRS, JGB, JQS, JFB, BSL, BJC.

Hence, the first option is correct.

2) Directions: How many triangles are there in the given figure?

1) 10

2) 13

3) 12

4) 11

Hint: To solve the reasoning triangle questions, firstly, label the given figure and determine the total number of triangles contained within it.

Solution

The given figure can be labelled as shown below –

Now, in the above figure, there are a total of 12 triangles. They are GFD, GBF, GDB, DFC, BFC, DBC, AEC, BAC, BGC, DGC, BAG, and BAF.

Hence, the third option is correct.

3) Directions: Find the total number of triangles in the figure.

1) 18

2) 24

3) 16

4) 26

Hint: Label the given figure and determine the total number of triangles contained within it.

Solution

The given figure can be labelled as shown below –

In the above-labelled figure, there are a total of 24 triangles. They are AED, AEB, CGD, CGB, AFD, AFB, CFD, CFB, ABC, ADC, ADG, ABG, CDE, CBE, DEF, EFB, BFG, GFD, DEB, EBG, BGD, DGE, ABD, CBD.

Hence, the second option is correct.

4) Directions: How many triangles are there in the given figure?

1) 18

2) 14

3) 19

4) 16

Hint: To solve the reasoning triangle questions, firstly, label the given figure and determine the total number of triangles contained within it.

Solution

The given figure can be labelled as shown below –

Now, in the above figure, there are a total of 19 triangles. They are ABC, CDE, EFG, GHI, ACP, PCN, CEN, NEL, GEL, GLJ, GIJ, PON, NML, LKJ, PDL, NFJ, AEO, EKI, CGM.

Hence, the third option is correct.

5) Directions: How many triangles are there in the given figure?

1) 20

2) 10

3) 18

4) 8

Hint: Label the given figure and then count the number of triangles in the labelled figure.

Solution

The given figure can be labelled as shown below –

Now, in the above figure, there are a total of 8 triangles. They are AOB, BOC, COD, AOD, ABC, BCD, ACD, ADB.

Hence, the fourth option is correct.

6) Directions: How many triangles are there in the given figure?

1) 20

2) 22

3) 24

4) 18

Hint: To solve the reasoning triangle questions, firstly, label the given figure and determine the total number of triangles contained within it.

Solution

The given figure can be labelled as shown below –

Now, in the above figure, there are a total of 20 triangles. They are AOB, AOD, COD, BOC, ACD, ABC, BCD, ABD, BEC, CFD, AGD, AHB, IEH, JGH, KFG, LEF, MIL, NKL, PKJ, OIJ.

Hence, the first option is correct.

7) Directions: How many triangles are there in the given figure?

1) 26

2) 24

3) 22

4) 28

Hint: Label the given figure and then count the number of triangles in the labelled figure.

Solution

The given figure can be labelled as shown below –

Now, in the above figure, there are a total of 24 triangles. They are AEF, FBG, GHC, DEH, EJI, FJK, GKL, LHI, MIN, MIQ, NIQ, JNO, POK, OSK, PKS, MPL, NQR, ORS, PTS, TQM, QRS, QST, IJK, IKL.

Hence, the second option is correct.

Preparation Tips for Figure Counting

Effective preparation for figure counting involves building strong observation skills, learning counting figures tricks, and practicing regularly. These tips will help you master counting of figures and reasoning questions with accuracy and speed.

How to Improve Speed in Counting Figures

Break diagrams into smaller parts, count shapes systematically, and use short methods for triangle counting questions with answers to save time.

Daily Practice Strategy for Figure Counting Reasoning

Solve a fixed set of counting figures questions daily, mixing easy and tricky diagrams to strengthen both accuracy and recognition skills.

Using Counting Figure Tricks for Accuracy

Apply proven counting figures tricks like symmetry detection, repeated pattern recognition, and layer-by-layer counting to avoid missing hidden shapes.

Common Mistakes to Avoid in Counting Figures

Avoid double-counting shapes and overlooking overlapping figures, especially in complex counting of figures reasoning questions.

Balancing Speed and Accuracy in Exams

Set a time limit for each counting figures reasoning problem, but double-check totals to prevent errors in competitive exam settings.

Verbal Reasoning Topics

Verbal reasoning topics evaluate your ability to understand, analyze, and logically interpret information presented in words or numbers. Key areas include distance and direction reasoning, arithmetic problems, seating arrangement, blood relation, missing number, series, inequality, order and ranking, verification of statements, coding-decoding, Venn diagrams, and syllogism, all essential for competitive exam success. The verbal reasoning topics are given below.

About the Faculty
Tanu Gupta, with over a decade of experience as a reasoning faculty, specializes in preparing students for various entrance examinations and career development. Her extensive work with multiple educational platforms and institutions has honed her expertise in logical and analytical thinking. Her dedication to innovative teaching methods ensures these articles provide practical insights and expert guidance.