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Q:

Find the number of triangles in the given figure.

A) 28 | B) 32 |

C) 36 | D) 40 |

Answer & Explanation Answer: C) 36

Explanation:

The simplest triangles are AML, LRK, KWD, DWJ, JXI, IYC, CYH, HTG, GOB, BOF, FNE and EMA i.e. 12 in number.

The triangles composed of two components each are AEL, KDJ, HIC and FBG i.e. 4 in number.

The triangles composed of three components each are APF, EQB, BQH, GVC, CVJ, IUD, DUL and KPA i.e. 8 in number.

The triangles composed of six components each are ASB, BSG, CSD, DSA, AKF, EBH, GGJ and IDL i.e. 8 in number.

The triangles composed of twelve components each are ADB, ABC, BCD and CDA i.e. 4 in number.

Total number of triangles in the figure = 12 + 4 + 8 + 8 + 4 = 36.

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Q:

Find the minimum number of straight lines required to make the given figure.

A) 11 | B) 14 |

C) 16 | D) 17 |

Answer & Explanation Answer: B) 14

Explanation:

The horizontal lines are AK, BJ, CI, DH and EG i.e. 5 in number.

The vertical lines are AE, LF and KG i.e. 3 in number.

The slanting lines are LC, CF, FI, LI, EK and AG i.e. 6 in number.

Thus, there are 5 + 3 + 6 = 14 straight lines in the figure.

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Q:

Choose the alternative which is closely resembles the water image of the given combination/figure.

**ADVANCE**

1) 2) 3) 4) NONE

A) 1 | B) 2 |

C) 3 | D) 4 |

Answer & Explanation Answer: B) 2

Explanation:

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Q:

What is the number of straight lines and the number of triangles in the given figure.

A) 10 straight lines and 34 triangles | B) 9 straight lines and 34 triangles |

C) 9 straight lines and 36 triangles | D) 10 straight lines and 36 triangles |

Answer & Explanation Answer: C) 9 straight lines and 36 triangles

Explanation:

The Horizontal lines are DF and BC i.e. 2 in number.

The Vertical lines are DG, AH and FI i.e. 3 in number.

The Slanting lines are AB, AC, BF and DC i.e. 4 in number.

Thus, there are 2 + 3 + 4 = 9 straight lines in the figure.

Now, we shall count the number of triangles in the figure.

The simplest triangles are ADE, AEF, DEK, EFK, DJK, FLK, DJB, FLC, BJG and LIC i.e. 10 in number.

The triangles composed of two components each are ADF, AFK, DFK, ADK, DKB, FCK, BKH, KHC, DGB and FIC i.e. 10 in number.

The triangles composed of three components each are DFJ and DFL i.e. 2 in number.

The triangles composed of four components each are ABK, ACK, BFI, CDG, DFB, DFC and BKC i.e. 7 in number.

The triangles composed of six components each are ABH, ACH, ABF, ACD, BFC and CDB i.e. 6 in number.

There is only one triangle i.e. ABC composed of twelve components.

There are 10 + 10 + 2 + 7 + 6+ 1 = 36 triangles in the figure.

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Q:

What is the number of triangles that can be formed whose vertices are the vertices of an octagon but have only one side common with that of octagon?

A) 64 | B) 32 |

C) 24 | D) 16 |

Answer & Explanation Answer: B) 32

Explanation:

When the triangles are drawn in an octagon with vertices same as those of the octagon and having one side common to that of the octagon, the figure will appear as shown in (Fig. 1).

Now, we shall first consider the triangles having only one side AB common with octagon ABCDEFGH and having vertices common with the octagon (See Fig. 2).Such triangles are ABD, ABE, ABF and ABG i.e. 4 in number.

Similarly, the triangles having only one side BC common with the octagon and also having vertices common with the octagon are BCE, BCF, BCG and BCH (as shown in Fig. 3). i.e. There are 4 such triangles.

This way, we have 4 triangles for each side of the octagon. Thus, there are 8 x 4 = 32 such triangles.

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Q:

Count the number of triangles and squares in the given figure.

A) 36 triangles, 7 Squares | B) 38 triangles, 9 Squares |

C) 40 triangles, 7 Squares | D) 42 triangles, 9 Squares |

Answer & Explanation Answer: C) 40 triangles, 7 Squares

Explanation:

The figure may be labelled as shown

**Triangles :**

The Simplest triangles are BGM, GHM, HAM, ABM, GIN, IJN, JHN, HGN, IKO, KLO, LJO, JIO, KDP, DEP, ELP, LKP, BCD and AFE i.e 18 in number

The triangles composed of two components each are ABG, BGH, GHA, HAB, HGI, GIJ, IJH, JHG, JIK, IKL, KLJ,LJI, LKD, KDE, DEL and ELK i.e 16 in number.

The triangles composed of four components each are BHI, GJK, ILD, AGJ, HIL and JKE i.e 6 in number.

Total number of triangles in the figure = 18 + 16 + 6 =40.

**Squares :**

The Squares composed of two components each are MGNH, NIOJ, and OKPL i.e 3 in number

The Squares composed of four components each are BGHA, GIJH, IKJL and KDEL i.e 4 in number

Total number of squares in the figure = 3 + 4 =7

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Q:

Find the number of triangles in the given figure ?

A) 5 | B) 8 |

C) 9 | D) 10 |

Answer & Explanation Answer: D) 10

Explanation:

The given figure can be labelled as :

The simplest triangles are AJF, FBG, HDI, GCH and JEI i.e 5 in number.

The triangles composed of the three components each are AIC, FCE, ADG, EBH and DJB i.e 5 in number.

Thus, there are 5 + 5 = 10 triangles in the given figure.

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Q:

Find the number of triangles in the given figure ?

A) 21 | B) 15 |

C) 18 | D) 20 |

Answer & Explanation Answer: A) 21

Explanation:

The simplest triangles are AKI, AIL, EKD, LFB, DJC, DKJ, KIJ, ILJ, JLB, BJC, DHC and BCG i.e. 12 in number.

The triangles composed of two components each are AKJ, ALJ, AKL, ADJ, AJB and DBC i.e. 6 in number.

The triangles composed of the three components each are ADC and ABC i.e. 2 in number.

There is only one triangle i.e. ADB composed of four components.

Thus, there are 12 + 6 + 2 + 1 = 21 triangles in the figure.

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