# counting figures reasoning questions with answers

Question 1:

How Many Triangles are there in the Given Figure?

45

Solution:

Number of blocks made by vertical line(x)=5=ABC, ACD, ADE, AEF and AFG
and Number of blocks made by horizontal line(y)=3=IBGK,HIKJ and AHJ
Therefore,
Number of triangles=[x*y(x+1)]/2
=[5*3(5+1)]/2
=[15(6)]/2
=90/2
=45

Question 2:

How Many Triangles are there in the Given Figure?

5

Solution:

Number of triangles embedded inside of the triangle, n = 1(ECF)
Number of horizontal blocks, m=1(BDFE)
Number of triangles=4n+m
=4*1+1
=4+1
=5

Question 3:

How Many Triangles are there in the Given Figure?

9

Solution:

Number of triangles embedded inside of the triangle, n = 2(BEC and GHI)
Number of horizontal blocks, m=1(BDFC)
Number of triangles=4n+m
=4*2+1
=8+1
=9

Question 4:

How Many Triangles are there in the Given Figure?

13

Solution:

Number of triangles embedded inside of the triangle, n = 3(ECF, GHI and JLK)
Number of horizontal blocks, m=1(BDFE)
Number of triangles=4n+m
=4*3+1
=12+1
=13

Question 5:

How Many Triangles are there in the Given Figure?

13

Solution:

Number of unit triangles in a side=3
Number of triangles=[x(x+2)(2x+1)]/8
=[3(3+2)(2*3+1)]/8
=[3*5(6+1)]/8
=[3*5*7]/8
=105/8
=13.125=13