How many triangles are there in the given figure ?

Options

A. 29
B. 38
C. 40
D. 35

Answer

C

Explanation

The simplest triangles are :
`Delta PNO, Delta PNM, Delta MPQ, Delta MOR, Delta AQP, Delta AQR, Delta BRA, Delta BRC, Delta SRC, Delta SCD, Delta SGR, Delta SGD, Delta DFG, Delta DFE: Delta TLM, Delta TJK, Delta TLK, Delta TIH,`
The triangles composed of two components are:
`Delta PON, Delta PMA, Delta APR: Delta RAM, Delta RAC: Delta RGC, Delta DGC, Delta DGE, Delta MPR, Delta GRD, Delta DCR, Delta TMK, Delta TKI, Delta TIG`
The triangles composed of four components are:
`Delta AMO, Delta AMC, Delta CAG, Delta CGE, Delta MKI, Delta GIK,`
Other triangles are: `Delta SPI, Delta DQK`
Total number of triangles 18 + 14 + 6 + 2 = 40