Question

What is a $50$ sided shape called?

Answer 1

Name of 50 sided polygon:

In geometry, a $50$ sided shape is called a Pentacontagon.

The number of diagonal of a polygon is $\frac{\mathbf{n}\left(n-3\right)}{\mathbf{2}}$.

The pentacontagon has $\frac{50\left(50-3\right)}{2}=1175$ diagonals.

We know that the sum of interior angles of a polygon is $\left(n-2\right)\mathbf{\times }\mathbf{180}\mathbf{°}$.

So, the sum of the interior angles of a Pentacontagon is,

$S=\left(50-2\right)\times 180°$

$\Rightarrow$ $S=\left(48\right)\times 180°$

$\Rightarrow$ $S=8640°$

Hence,50 sided shape is called as Pentacontagon.