Counting of Figures - Expert Level
Practice and master this topic with our carefully crafted questions.
Challenge yourself with expert-level counting of figures questions featuring complex, overlapping and mixed shapes. Improve observation, accuracy and problem-solving speed.
The maximum number of squares in the given figure is
🔍 Analyze the Pattern
On carefully observing the labelled figure:
◻ Count the Squares
The squares can be counted according to their sizes:
- 1 × 1 Squares (9): AGPF, GHOP, HBIO, FENP, HIMO, ENLM, MJKI, LKCM, EDCJ
- 2 × 2 Squares (4): AHNE, GBJO, FLKD, PICJ
- 3 × 3 Square (1): ABCD
Total Squares = 9 + 4 + 1 = 14
📐 Quick Formula Method
For an 3 × 3 square grid, the total number of squares is calculated as:
1² + 2² + 3²
= 9 + 4 + 1
= 14 Squares
General Formula:
1² + 2² + 3² + ... + n²
where n is the number of small squares on one side.
Correct Answer: Option (D) — 14 Squares
How many triangles are there in the figure PQRS ?
🔍 Analyze the Pattern
On carefully observing the labelled figure:
🔺 Count the Triangles
The triangles present in the figure are:
PAE, ADE, AQE, QBE, DEC, CES, BER, ECR, PDE, EQD, ESR, PRB, PSQ, PQR, PSR, SQR
Total Triangles = 16
Correct Answer: Option (A) — 16 Triangles
How many squares are there in the square figure ABCD ?
🔍 Analyze the Pattern
On carefully observing the labelled figure:
◻ Count the Squares
The squares present in the figure are:
- 1 × 1 Squares (16): AQOP, ERUQ, FSVR, GBHS, TOWN, UXWT, VYXI, DMXW, QRET, RSVU, STVH, WXLM, XYKL, OPND, HIJC, ICKJ
- 2 × 2 Squares (9): AEUO, EFVR, FGHS, PWTD, RXYL, SVIK, ARTD, EXVL, FSKC
- 3 × 3 Squares (4): AFXO, EGYL, PBID, RHJC
- 4 × 4 Square (1): ABCD
Total Squares = 30
📐 Quick Formula Method
For a 4 × 4 square grid:
1² + 2² + 3² + 4²
= 16 + 9 + 4 + 1
= 30 Squares
where n = 4 (number of small squares on one side)
Correct Answer: Option (4) — 30 Squares
How many triangles are there in the given figure ?
🔍 Analyze the Pattern
On carefully observing the labelled figure:
🔺 Count the Triangles
The triangles present in the figure are:
EIB, EIA, AIM, ABM, BIM, EAB, HLA, HLD, LDA, ADM, DKM, DKC, KCM, DCM, GKC, GKB, BJF, BJC, CJF, CFM, BCF, HDA, HDB, HFG, EFH, EFG, GHF, EHG
Total Triangles = 28
Correct Answer: Option (B) — 28 Triangles
How many triangles are there in the following figure ?
🔍 Analyze the Pattern
On carefully observing the labelled figure:
🔺 Count the Triangles
The triangles present in the figure are:
🔺 ABC; 🔺 ABE; 🔺 ACE; 🔺 ABD; 🔺 ACF; 🔺 ABD; 🔺 BCD; 🔺 AFG; 🔺 ADG; 🔺 BFG; 🔺 BEG; 🔺 CEG; 🔺 CDG; 🔺 ACG; 🔺 ABG; 🔺 BCG
Total Triangles = 16
Correct Answer: Option (A) — 16 Triangles
How many rectangles are there in the given figure ?
🔍 Analyze the Pattern
On carefully observing the labelled figure:
▭ Count the Rectangles
The rectangles present in the figure are:
AEML, LMOK, AEOK, KNJD, NOIJ, KOID, AEID, LMID, EFPO, FBGP. EBGO, OGHQ, QHCI, OGCI, EBHQ, EBCI, AFPK, ABGK, NGCJ, KGCD, ABCD.
Total Rectangles = 21
Correct Answer: Option (C) — 21 Rectangles
How many rectangles are there in the figure given ?
🔍 Analyze the Pattern
On carefully observing the labelled figure:
▭ Count the Rectangles
The rectangles present in the figure are:
ABCD, AEJK, AFIK, ABGK, EFIJ, EBGJ, FBGI, FBCH, IGCH, AFHD, KIHD
Total Rectangles = 11
Correct Answer: Option (4) — 11 Rectangles
How many triangles are there in the following figure ?
🔍 Analyze the Pattern
On carefully observing the labelled figure:
🔺 Count the Triangles
The triangles present in the figure are:
🔺ABC ; 🔺ABD ; 🔺ADC ; 🔺AFC; 🔺FDC ; 🔺AFB ; 🔺FDB ; 🔺FBC; 🔺GBD ; 🔺ADE ; 🔺GBE ; 🔺FDG; 🔺DBE ;
Total Triangles = 13
Correct Answer: Option (B) — 13 Triangles
How many triangles are there in the following figure ?
🔍 Solution
After carefully observing the labelled figure, count the triangles from the smallest to the largest.
🔺 Small Triangles (16)
AGH, AHB, BHI, BIC, GHI, HIB, EGJ, GJE, JID, IDC, GJI, JID, FAG, FGE, BCI, ICD
🔺 Medium Triangles (8)
ABI, AGI, EGD, GCD, FAE, BCD, FGI, GIC
🔺 Large Triangles (4)
FAB, ABC, FED, EDC
Total Triangles = 16 + 8 + 4 = 28
✅ Correct Answer: Option (C) — 28 Triangles
How many triangles are there in the following figures?
🔍 Solution
After carefully observing the labelled figure, count the triangles from the smallest to the largest.
🔺 Small Triangles (16)
ADE, DEG, DGE, FJG, FGJ, EGH, GHK, GKL, IJM, JMN, JNK, KNO, KOL, LOC, BIM, HOC
🔺 Medium Triangles (7)
DFE, FGH, IJK, JKL, FKN, GKO, IMN
🔺 Large Triangles (3)
AFH, DLC, BEC
🔺 Largest Triangle (1)
ABC
Total Triangles = 16 + 7 + 3 + 1 = 27
✅ Correct Answer: Option (B) — 27 Triangles