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Counting of figure is the realization of different geometrical figures from complex figure. This topic is generally designed to test analytical ability of the candidate.

Counting of lines/straight line

Straight line can be of three types:

Rule: Straight line is set of points that extends endlessly in both direction

On counting it will be counted as one line. XY and not two straight lines XP and PY

Q1). How many straight lines are there in given figure?

Ans. Find all types of straight line simply

  1. Horizontal Line = AB + HF + DC = 3
  2. Vertical Line = AD + EG +BC = 3
  3. Slant line = AC + BD = 2

Total straight lines = 3+3+2=8


Counting Triangles

Q2). Find the number of Triangle in following figures?

Answer

Rules for Counting Triangle

  1. Smallest triangles are counted first.
  2. At the second step these triangles are formed with the two triangles and further counting goes in the same way i.e. triangle formed with three, four……triangles are counted one after another.
  3. Largest triangle is counted at the final step

(i)

Smallest triangle = △ABD +△ADC = 2

Largest triangle = △ABC = 1

Total = 1 + 2 = 3


(ii)

Smallest triangle = △ABC +△ACD+△ADE = 3

Triangles formed with these three △

△ABD +△ACE = 2

Largest triangle = △ABC = 1

Total = 3 + 2 + 1 = 6

Short Trick: 

Find the part of triangle and add them

Means Total △ = 1 + 2 + 3 = 6


(iii)

Total △ = 1+2+3+4=10

(iv)

Short Trick

Total no of △= No of part of △ × No of partitions

No of part of △ = 1+2 = 3

No of partitions = 2 (i.e. D1 & D2)

Total no of △= 3 × 2 = 6


(v)

Short Trick:

Total no of △= No of part of △ × No of partitions

No of part of △ = 1+2 + 3= 6

No of partitions = 3 (i.e. D1, D2 & D3)

Total no of △= 6 × 3 = 18


(vi)

Short Trick:

Total no of △= No of part of △ × No of partitions

No of part of △ = 1+2 + 3 + 4= 10

No of partitions = 3 (i.e. D1, D2, D3)

Total no of △= 10 × 3 = 30


(vii)

7 triangles is the Ans.


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