The First Part of the Chapter includes the problems based on the counting of the figures in a Given Complex Figures and the second part of the chapter based on the Hidden embedded Figures which are inside the question Figure. The Systematic method for determining the number of any particular Figure or the Hidden figure from the answer figures would be clear from the examples.

Example:- 1- How many Triangles and Straight lines are there ?

(a) 8, 20 (b) 8, 22 (c) 10, 22 (d) 10, 20
Solution:– Lets name the Figure First.

No. of Straight lines: AB, BC, CA, AD, AE, GD, GC, DF = 8
No. of Triangles: ABC, ABD, ADE, AEC, ABE, ADC, AGC, BGC, BGD, DGC, GDH, HDI, GDI, DIE, IEC, DIC, AIC, AIJ, JIC, AGI, AGH, AHI = 22
Hence option (b)

Example: 2 How many Triangles are there in the following Figure?

Solution: Lets name the Figure First.

Number of triangles are ABC, ADC, ADB, BDC, DOC, COB, BOA, AOD, DOE, EOC, AOF, FOB, DOG, COH, AOG, BOH.
Total: 16

Direction 2-3: How many Triangles are there?

(a) 20 (b) 22 (c) 24 (d) 26

Solution:-

Total Number of triangles:
From the Vertex A: ABC, AJF, AKE, ALD
From the Vertex B: BIJ, BHK, BGL
From the Vertex C: CGF, CHE, CID
In quad BJFC: there are 7 small triangles
In quad KEJF: there are 4 Small triangles
In quad KELD: there are three triangles
Total triangles 24.
Option (c)

(a) 15 (b) 16 (c) 18 (d) 19

Solution:-

Number of Triangle are ABG, AJC, KFD, DIB, AIH, KIJ, BJF, CFG, DGH, JFG, IJG, HJG, IOH, IOJ, IOG, HOG.
Total: 19
Option (d)

Direction 5-6: How many quadrilaterals are there in these given figures?

Solution:-

TOTAL NUMBER OF QUADRILATERALS = 17
Hence option (c)

Solution:-

Direction 7-9: Count the total number of Triangles of the following figures?

Solution:-There are total 24 triangles. The way to count the triangles of the figure is to draw the figure and count.
Option(c)

Solution:- Option: (c)

Solution:- The total number of triangles present in the above figure is 20.
Option (d)

Direction 10-11: How many squares and triangles are there in the given figures?

Solution:-

The above figure contains 4 boxes were two are
Similar.

This particular box contains 8 triangles and 1 square, as there are two boxes which are same, than there are total 16 triangles and 2 squares.

The above figure contains – (16 triangles and 3 squares) x 2 = 32 triangles and 6 squares.
Total triangles = 48 and total squares = 8
Hence option (b)

Solution:- Total triangles are - 22 and total squares are 5.
Hence option (a)