## Definition of a Polygon

A polygon is a two-dimensional geometric shape that is made up of straight lines called edges, that connect a series of points called vertices. The edges and vertices of a polygon form its boundary. A polygon must have at least three sides (edges) and three vertices.

## Types of Polygons

Polygons can be classified based on the number of sides and angles they have. Based on the number of sides, some common polygons include:

- triangles (three sides),
- quadrilaterals (four sides),
- pentagons (five sides),
- hexagons (six sides),
- heptagons (seven sides),
- octagons (eight sides),
- and nonagons (nine sides).

## Area Of Polygon

The area of a polygon is the measurement of the region enclosed by the sides of the polygon. The area of a polygon can be find using various methods, depending on the shape of the different types of polygon .

**For example,** the area of a regular polygon can be calculated using the formula:

**Area of Regular Polygons = (perimeter * apothem) / 2**

where the perimeter is the total length of all sides of the polygon, and the apothem is the distance from the center of the polygon to the midpoint of any one of its sides.

## How to Find Area of Polygon with N-sides?

To find the area of a polygon with n-sides, you can use the following formula:

Where:

- N is the number of sides in the polygon
- s is the length of one side of the polygon
- π is the mathematical constant pi (approximately equal to 3.14159…)
- tan is the tangent function, which can be found on most scientific calculators

Here are the steps to use the formula to find the area of a polygon with n-sides:

- Measure the length of one side of the polygon, which is denoted by s.
- Count the number of sides in the polygon, which is denoted by n.
- Plug in the values of n and s into the formula
- Use a scientific calculator to find the value of tan(π/N). Make sure the calculator is in radian mode.
- Multiply the values of N, s, and tan(π/N) together, and then divide the result by 4 to get the area of the polygon.