Question

What is an eight-sided polygon called?

Answer 1

Hint: We define the concept of a n-sided polygon. We also find the relation between its sides, angles and vertices. We place the value of 8 in place of n to find the octagon. We also define the concept of a regular polygon and regular octagon.

Complete step by step solution:
An eight-sided polygon is called an octagon.
An octagon has 8 vertices and 8 sides.
We know that to form a triangle we need three points which are non-linear.
We also have that no three points out of those 8 vertices are non-linear.
The octagon is an 8-sided polygon. In general, a polygon is termed an n-sided polygon.
The number of sides of a polygon is equal to the number of vertices and number of angles.
Therefore, the octagon also has 8 angles.

The difference between a normal polygon and regular polygon is the symmetry of the sides, the angles and the overall shape of the polygon.

Note: In case of a regular polygon the value of the interior angles is ${\displaystyle \frac{\pi (n-2)}{n}}$ and the exterior angle is ${\displaystyle \frac{2\pi }{n}}$. The lengths can be different to each other and the same goes the angles. They are not bound to be equal. But if they are equal then the both of them go together to be equal. In that case the polygon is called a regular polygon.