Question

Count the number of triangles in the figure.

• A. 40
• B. 48
• C. 30
• D. 50

Answer 1

Answer: (B)

48

Let us count the number of triangles vertex wise.
From vertex $1$, we can count $4$ triangles.
From vertices $2$ and $3$, we can count $3$ triangles each.
From vertices $4,5,6$, we have $2$ triangles each.
Finally, from vertices, $7,8,9,10$, we have $1$ triangle each.
We thus have $4\times 1+3\times 2+2\times 3+1\times 4=40$ triangles.
These are however, upright triangles only.
From vertices $12,13,14$ we have $1+2+1=4$ triangles in inverted shapes.
From $8,9$, we have $1$ triangle each and from $5$, we have 1 triangle.
Thus, total no. of inverted triangles $=7$
Hence, total no. $20+7=27$
Extending this pattern of counting, let us count the triangles in fig.
Upright triangles $=5\times 1+4\times 2+3\times 3+2\times 4+1\times 5=35$
Inverted triangles $=(1+2+2+1)+(1+2+1)+(1+1)+1=13$
Hence total number $=48$
Hence, option $B$ is the correct answer.