Question

How many diagonals are there in an octagon?

Answer 1

Calculate the number of diagonals:

The number of diagonals in an $n$ sided polygon is given as,

${\mathit{D}}_{\mathbf{n}}\mathbf{=}\frac{\mathbf{n}\left(n-3\right)}{\mathbf{2}}$

An octagon has $8$ sides, i.e., $n=8$.

Thus, the number of diagonals in an octagon is,

$\begin{array}{cl}& D_8=\frac{8(8-3)}{2}\\ \Rightarrow & D_8=4\times 5\\ \Rightarrow & D_8=20\end{array}$

Therefore, the number of diagonals in an octagon is $20$.