1.  Find the number of triangles in the given figure ?

10
19
21
23

```Answer

The simplest triangles are ABI, BIC, AIJ, GIJ, AHJ, CDJ, JHG, JDE, GJF and EJF i.e. 10 in number.
The triangles composed of two components each are ABC, BCJ, ACJ, BAJ, AJG, CJE and GJE i.e. 7 in number.
The triangles composed of four components each are ACG, ACE, CGE and AGE i.e. 4 in number.
Total number of triangles in the figure =10+ 7 + 4 = 21. ```

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2.  Find the number of triangles in the given figure

10
12
14
16

```Answer

The simplest triangles are ABJ, ACJ, BDH, DHF, CIE and GIE i.e. 6 in number.
The triangles composed of two components each are ABC, BDF, CEG, BHJ, JHK, JKI and CJI i.e. 7 in number.
There is only one triangle JHI which is composed of four components.
Thus, there are 6 + 7 + 1 = 14 triangles in the given figure. ```

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3.  How many rectangles are there in the given figure ?

10
9
8
7

```Answer

The simplest rectangles are ABJI, BCKJ, IJFG and JKEF i.e. 4 in number.
The rectangles composed of two components each are ACKI, BCEF, IKEG and ABFG i.e. 4 in number.
The only rectangle composed of four components is ACEG.
Thus, there are 4 + 4 + 1 = 9 rectangles in the given figure. ```

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

10 straight lines and 34 triangles
9 straight lines and 34 triangles
9 straight lines and 36 triangles
10 straight lines and 36 triangles

```Answer

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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5.  Find the number of triangles in the given figure ?

11
13
15
17

```Answer