Area of Regular Polygon - Definition, Formula and Examples

What Is A Polygon?

A closed, two-dimensional shape composed of straight lines is known as a polygon in geometry. Each side must bisect exactly two other sides, but only at their ends. Polygons must have a common endpoint and noncollinear sides. We are aware that a triangle is a polygon with the least sides. Basically, the polygon can be categorized as either convex or concave and regular or irregular. Any polygon with equal sides and interior angles is said to be regular. The method used to determine the area of regular polygons is based on the corresponding formulas for each polygon. Remember that an n-gon is a polygon with n sides.

The Formula For Calculating A Regular Polygon's Surface Area

For some of the most popular polygons, the formulas for the area of regular polygons are as follows:

• Area of an equilateral triangle = \frac{\sqrt{3}}{4}a^{2}

Here "a" denotes the triangle's equilateral triangle's side length.

• Area of a Square = a^{2}

Here "a" denotes the square's side length.

• Regular Pentagon’s Area = \frac{1}{4}\sqrt{[5(5+2\sqrt{5}]}a^{2}

Here "a" is the pentagon's side length.

• Regular Hexagon’s Area = \frac{3\sqrt{3}}{2}a^{2}

Here "a" denotes the hexagon's side length.

The Area Of A Regular Polygon With N Sides Formula

When a polygon has "n" sides, the following formula can be used to determine its area:

The formula for Area of Regular Polygons = \frac{l^{2}n}{4\tan\frac{180}{n}}

Here "l" denotes the polygon's side length.

A Regular Polygon's Area Inside A Circle

According to the following formula, the area of a regular polygon encircled by a circle is:

Area of a regular polygon encircled by a circle = \frac{nr^{2}}{2}\sin\frac{2\pi}{n}

Here "n" denotes the number of sides and “r” denotes the circumradius.

Properties Of Polygon

• Finding an apothem allows one to determine the area of a regular polygon given the length of one side.

• Apothem divides a side into two equal portions by falling at a right angle on its center.

• A square is a regular polygon with four sides, whereas an equilateral triangle has three sides. They are not prefixed as regular before the form name as a result.

• The total interior angle of an n-sided polygon is (n-2)\times180^{o}

• An n-sided regular polygon's inner angles are measured in terms of angles as: (n-2)\times\frac{180}{n}

• Each exterior angle of an n-sided regular polygon's angle measures \frac{360^{o}}{n}

• The number of diagonals in an n-sided polygon = \frac{n(n-3)}{2}

• The number of triangles generated when a polygon's diagonals are connected from one corner = n-2