The question is attchad. Please   send step by step complete solution. Please do not send any Web link to this question because I am unable to conmnect the same and open the solution every time.

Asked by sudhanshubhushanroy | 14th Dec, 2017, 07:17: AM

Expert Answer:

begin mathsize 16px style straight A space polygon space with space straight n space sides space will space have space straight n space vertices.
We space will space have space three space cases colon
left parenthesis straight i right parenthesis
Having space two space sides space common
left parenthesis ii right parenthesis
Having space one space side space common
left parenthesis iii right parenthesis
Having space no space side space common
Total space number space of space triangles space formed space will space be space straight C presuperscript straight n subscript 3.
Total space number space of space triangles space having space no space side space common
equals Total space number space of space triangles space formed space minus having space two space sides space common space minus space having space one space side space common space
equals space straight C presuperscript straight n subscript 3 space minus space straight n space minus space straight n space straight C presuperscript straight n minus 4 end presuperscript subscript 1
equals space straight C presuperscript straight n subscript 3 space minus space straight n space minus space straight n space left parenthesis straight n minus 4 right parenthesis end style

Answered by Sneha shidid | 18th Dec, 2017, 04:17: PM