Question

Find the number of triangles in the given figure.

Figure:

Answer 1

Find the number of triangles in the given figure.

To find the number of triangles we will label the given figure.

Then, in the following diagram, we will count and add all of the small and large triangles.

From the above diagram, the triangles are formed by combining $3$ points and having $3$ sides or edges. Various small and large triangles are made by combining small geometrical shapes in the figure itself.

There are total five small triangles are, $∆\mathrm{KPQ},∆\mathrm{OPT},∆\mathrm{NTS},∆\mathrm{MSR}$ and $∆\mathrm{LQR}$.

There are total five large triangles are, $∆\mathrm{LSO},∆\mathrm{KRN},∆\mathrm{QMO},∆\mathrm{PLN}$ and $∆\mathrm{KMT}$.

Therefore,

Total number of triangles $=$ Number of small triangles $+$ Number of large triangles

$=5+5$

$=10$

Hence, the given figure contains $10$ triangles.