Question

Study the given figure and answer the questions .
Count the number of triangles in the figure.

• A. $12$
• B. $16$
• C. $22$
• D. $24$

Answer 1

The correct option is C $22$

$\Rightarrow$ The simplest triangles are $△ABC,△CDE,△FGH,△HIJ,△ACK,△CHK,△JHK,△AJK,△CEL,△EFL,△FHL,△CHL$ i.e $12$ in numbers.

$\Rightarrow$ The triangles composed of two components each are $△ACJ,△CHJ,△AJH,△ACH,△CEH,△EFH,△CHF,△CEF$ i.e $8$ in numbers.

$\Rightarrow$ The triangles composed of three components each are $△CFJ,△AEH$ i.e. $2$ in numbers.

$\Rightarrow$ Total number of triangles in the figure = $12+8+2=22$