(i) Number of diagonals in Heptagon is
\(=n\,\times\frac{n\,-\,3}{2}\) [n represents number of sides]
\(=7\times\frac{7\,-\,3}{2}\)
\(=7\times\frac{4}{2}\)
= 14
So, Number of diagonals in heptagon is 14.
(ii) Number of diagonals in Octagon is
\(=n\,\times\frac{n\,-\,3}{2}\) [n represents number of sides]
\(=8\times\frac{8\,-\,3}{2}\)
\(=8\times\frac{5}{2}\)
= 20
So, Number of diagonals in octagon is 20.
(iii) Number of diagonals in polygon of 12 sides is
\(=n\,\times\frac{n\,-\,3}{2}\) [n represents number of sides]
\(=12\times\frac{12\,-\,3}{2}\)
\(=12\times\frac{9}{2}\)
= 54
So, Number of diagonals in polygon of 12 sides is 54.
