A polygon having equal sidesâ€™ i.e. equilateral and equal angles i.e. equiangular is known as a regular polygon. An apothem is used to find the area of a regular polygon. Apothem is a segment that joins the polygonâ€™s center to the midpoint of any side and it is perpendicular to that side. All vertices of a regular polygon lie on a common circle (the circumscribed circle), i.e., they are concyclic points. That is, a regular polygon is a cyclic polygon. Along with it, the property of equal-length sides, this implies that every regular polygon also has an inscribed circle or incircle that is tangent to every side at the midpoint. Thus, a regular polygon is a tangential polygon.

A regular n-sided polygon can be constructed with compass and straightedge if and only if the odd prime factors of n are distinct Fermat primes. See constructible polygon.

**The formula forÂ area of a regular polygon** is given as,

**A =** Â **$\frac{l^{2}n}{4tan(\frac{\pi }{n})}$**

Where,

l is the side length

n is the number of sides

### Solved Examples

**QuestionÂ 1:**Calculate the area of 5 sided polygon with a side length 4Â cm ?

**Solution:**

l = 4Â cm and n = 5

The formula for finding the area is,

^{2}