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- Question
Count the number of parallelogram in the given figure.
Options- Correct Answer
- 18
ExplanationThe figure may be labelled as shown.
The simplest ||gms are ABFE, BCGF, CDHG, EFJI, FGKJ and GHLK. These are 6 in number.
The parallelograms composed of two components each are ACGE, BDHF, EGKI, FHLJ, ABJI, BCKJ and CDLK. Thus, there are 7 such parallelograms.
The parallelograms composed of three components each are ADHE and EHLI i.e. 2 in number.
The parallelograms composed of four components each are ACKI and BDLJ i.e. 2 in number
There is only one parallelogram composed of six components, namely ADLI.
Thus, there are 6 + 7 + 2 + 2 + 1 = 18 parallelograms in the figure.
More questions
- 3. Find the number of triangles in the given figure.
Options
Discuss
Correct Answer: 28
Explanation:
The figure may be labelled as shown.
The simplest triangles are AFJ, FJK, FKB, BKG, JKG, JGC, HJC, HIJ, DIH, DEI, EIJ and AEJ i.e. 12 in number.
The triangles composed of two components each are JFB, FBG, BJG, JFG, DEJ, EJH, DJH and DEH i.e. 8 in number.
The triangles composed of three components each are AJB, JBC, DJC and ADJ i.e. 4 in number.
The triangles composed of six components each are DAB, ABC, BCD and ADC i.e. 4 in number.
Thus, there are 12 + 8 + 4 + 4 = 28 triangles in the figure.
- 5. Choose the figure which is different from the rest.
(1) (2) (3) (4) (5)
Options
Discuss
Correct Answer: 4
Explanation:
The inclination of the triangle is different in fig. (4).- 6. Select the alternative which represents three out of the five alternative figures which when fitted into each other would form a complete square.
Options
Discuss
Correct Answer: 123
Explanation:
- 7. Find the question mark
? figure from answer figure:
Options
Discuss
Correct Answer: 2
Explanation:
The second figure is water image of the first figure.
- 9. Select the figure which satisfies the same conditions of placement of the dots as in Figure-X.
Options
Discuss
Correct Answer: 4
Explanation:
In fig. (X), one of the dots lies in the region common to the circle and the rectangle only, another dot lies in the region common to the circle, the square and the rectangle only and the third dot lies in the region common to the circle, the square and the triangle only. In each of the figures (1) and (3) there is no region common to the circle, the square and the rectangle only and in fig. (2), there is no region common to the circle, the square and the triangle only. Only, fig. (4) consists of all the three types of regions.- 10. Count the number of triangles and squares in the given figure.
Options
Discuss
Correct Answer: 32 triangles, 10 squares
Explanation:
The figure may be labelled as shown.
Triangles :
The simplest triangles are IJQ, JKQ, KLQ, LMQ, MNQ, NOQ, OPQ and PIQ i.e. 8 in number. The triangles composed of two components each are ABQ, BCQ, CDQ, DEQ, EFQ, FGQ, GHQ, HAQ, IKQ, KMQ, MOQ and OIQ i.e. 12 in number.
The triangles composed of four components each are ACQ, CEQ, EGQ, GAQ, IKM, KMO, MOI and OIK i.e. 8 in number.
The triangles composed of eight components each are ACE, CEG, EGA and GAC i.e. 4 in number.
Total number of triangles in the figure = 8 + 12 + 8 + 4 = 32.
Squares :
The squares composed of two components each are IJQP, JKLQ, QLMN and PQNO i.e. 4 in number.
The squares composed of four components each are ABQH, BCDQ, QDEF and HQFG i.e. 4 in number.
There is only one square i.e. IKMO composed of eight components.
There is only one square i.e. ACEG composed of sixteen components.
Thus, there are 4 + 4 + 1 + 1= 10 squares in the given figure.
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- 3. Find the number of triangles in the given figure.