How many triangles are there?

Question: How many triangles are there?



Solution:


The simplest triangles are AFB, FEB, EBC, DEC, DFE, and AFD so, 6 triangles.
The triangles are composed of two components: AEB, FBC, DFC, ADE, DBE, and ABD so, 6 triangles
The triangles composed of three components are ADC and ABC so, 2 trangles.
There is only one triangle DBC which is composed of four components.

Thus, there are 6 + 6 + 2 + 1 = 15 triangles in the figure.